Feasibility of forecasting highway safety in support of safety incentive and safety target programs

Feasibility of Forecasting Highway
Safety in Support of Safety
Incentive and Safety Target
Programs
Final Report 597
Prepared by:
Simon Washington, Ph. D.
and
Do- Gyeong Kim
Department of Civil and Environmental Engineering
Arizona State University
Tempe, Arizona
November 2007
Prepared for:
Arizona Department of Transportation
206 South 17th Avenue
Phoenix, Arizona 85007
and
Arizona Governor’s Office of Highway Safety
In cooperation with
U. S. Department of Transportation
Federal Highway Administration
National Highway Traffic Safety Administration
The contents of this report reflect the views of the authors who are responsible for the
facts and the accuracy of the data presented herein. The contents do not necessarily
reflect the official views or policies of the Arizona Department of Transportation or the
Federal Highway Administration. This report does not constitute a standard, specification,
or regulation. Trade or manufacturers' names which may appear herein are cited only
because they are considered essential to the objectives of the report. The U. S.
Government and the State of Arizona do not endorse products or manufacturers.
Technical Report Documentation Page
1. Report No.:
FHWA- AZ- 06- 597
2. Government Accession No. 3. Recipient’s Catalog No.
4. Title and Subtitle
Feasibility of Forecasting Highway In Support of Safety Incentive
and Safety Target Programs
5. Report Date:
November 2007
6. Performing Organization Code
7. Authors: Drs. Simon Washington and Do- Gyeong Kim 8. Performing Organization Report No.
9. Performing Organization Name and Address
Arizona State University
Department of Civil & Environmental Engineering
Tempe, AZ 85287- 5306
10. Work Unit No.
11. Contract or Grant No.
SPR- PL- 1-( 61) 597
12. Sponsoring Agency Name and Address
Arizona Department of Transportation
206 S. 17th Avenue
Phoenix, AZ 85007
13. Type of Report & Period Covered
Final Report
14. Sponsoring Agency Code
15. Supplementary Notes:
Prepared in cooperation with the Arizona Governor’s Office of Highway Safety and the U. S.
Department of Transportation, Federal Highway Administration & National Highway Traffic
Safety Administration
16. Abstract
Using the frequency of fatal crashes from the current observation period ( e. g. month, year, etc.) as the
prediction of expected future performance does not account for changes in safety that result from
increases in exposure ( population, additional roads, new drivers, etc.). This effect is especially
pronounced in rapidly growing regions, where safety changes are anticipated in the absence of safety
investment programs. The objective of this study was to examine the feasibility of predicting future
fatal motor vehicle crashes given changes in future risk exposure, so that reasonable safety ‘ targets’
can be established in support of a safety incentive or safety target programs. Safety incentive or
target programs can be used to set future safety targets ( i. e. fatal crashes) for jurisdictions in Arizona.
17. Key Words
Safety forecasting, fatal crashes, safety
planning, safety management
18. Distribution Statement
Document is available to the
U. S. public through the
National Technical Information
Service, Springfield, Virginia
22161
23. Registrant’s Seal
19. Security Classification
Unclassified
20. Security Classification
Unclassified
21. No. of Pages
41
22. Price
SI* ( MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By To Find Symbol
LENGTH LENGTH
in inches 25.4 millimeters mm mm millimeters 0.039 inches in
ft feet 0.305 meters m m meters 3.28 feet ft
yd yards 0.914 meters m m meters 1.09 yards yd
mi miles 1.61 kilometers km km kilometers 0.621 miles mi
AREA AREA
in2 square inches 645.2 square millimeters mm2 mm2 Square millimeters 0.0016 square inches in2
ft2 square feet 0.093 square meters m2 m2 Square meters 10.764 square feet ft2
yd2 square yards 0.836 square meters m2 m2 Square meters 1.195 square yards yd2
ac acres 0.405 hectares ha ha hectares 2.47 acres ac
mi2 square miles 2.59 square kilometers km2 km2 Square kilometers 0.386 square miles mi2
VOLUME VOLUME
fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ounces fl oz
gal gallons 3.785 liters L L liters 0.264 gallons gal
ft3 cubic feet 0.028 cubic meters m3 m3 Cubic meters 35.315 cubic feet ft3
yd3 cubic yards 0.765 cubic meters m3 m3 Cubic meters 1.308 cubic yards yd3
NOTE: Volumes greater than 1000L shall be shown in m3.
MASS MASS
oz ounces 28.35 grams g g grams 0.035 ounces oz
lb pounds 0.454 kilograms kg kg kilograms 2.205 pounds lb
T short tons ( 2000lb) 0.907 megagrams
( or “ metric ton”)
mg
( or “ t”)
mg megagrams
( or “ metric ton”)
1.102 short tons ( 2000lb) T
TEMPERATURE ( exact) TEMPERATURE ( exact)
º F Fahrenheit
temperature
5( F- 32)/ 9
or ( F- 32)/ 1.8
Celsius temperature º C º C Celsius temperature 1.8C + 32 Fahrenheit
temperature
º F
ILLUMINATION ILLUMINATION
fc foot candles 10.76 lux lx lx lux 0.0929 foot- candles fc
fl foot- Lamberts 3.426 candela/ m2 cd/ m2 cd/ m2 candela/ m2 0.2919 foot- Lamberts fl
FORCE AND PRESSURE OR STRESS FORCE AND PRESSURE OR STRESS
lbf poundforce 4.45 newtons N N newtons 0.225 poundforce lbf
lbf/ in2 poundforce per
square inch
6.89 kilopascals kPa kPa kilopascals 0.145 poundforce per
square inch
lbf/ in2
SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380
Table of Contents
Motivation for Study............................................................................................................ 1
Background and Relevant Research .................................................................................... 3
Data Collection and Description.......................................................................................... 5
Methodological Approach and Modeling Results ............................................................. 17
Procedure to Apply the Safety Incentive or Safety Target Forecasting Model ................. 21
Conclusions and Recommendations .................................................................................. 23
Appendix A: Questionnaire Sent to Jurisdictions.............................................................. 27
Appendix B: Arizona Population and Population Change Statistics
by Jurisdiction ( 2000) ................................................................................ 28
Appendix C: Arizona Population Density by Jurisdiction ( 2000) ..................................... 31
References..................................................................................................................... .... 35
List of Tables
Table 1: Description and Measurement of Variables Used in the Analysis ........................ 6
Table 2: The Percent Change in Arizona Population from 1990 to 2000 by County.......... 7
Table 3: Arizona Land Areas by County in 2000 ................................................................ 9
Table 4: Arizona Population Densities by County in 2000 ............................................... 10
Table 5: Arizona Population of Elderly, Young, and Minorities by County in 2000........ 11
Table 6: Arizona Number of Housing Units, Density, and Persons per Household
by County in 2000............................................................................................... 12
Table 7: Arizona Number of Employees and Mean Travel Time to Work
by County in 2000............................................................................................... 13
Table 8: Arizona Total and Fatal Crashes by Jurisdiction in 2000.................................... 14
Table 9: Negative Binomial Model Estimation Results of Fatal Crashes
with Complete Set of Predictors ......................................................................... 19
Table 10: Three New Fatal Crash Models and Comparison
to Previously Estimated Models ...................................................................... 20
Table 11: Example 1: Excel Prediction Spreadsheet for Fatal Crash Prediction Model ... 21
Table 12: Example 2: Excel Prediction Spreadsheet for Fatal Crash Prediction Model ... 22
Table 13: Description of Important Predictor Variables for Safety Forecasting Model.... 24
List of Figures
Figure 1: Location of Counties and COGs/ MPOs in Arizona ............................................. 5
Figure 2: Percentage of Total Arizona Population by County in 2000................................ 8
Figure 3: Correlation Matrix of Predictor Variables.......................................................... 18
List of Acronyms
ADOT Arizona Department of Transportation
AADT Annual Average Daily Traffic
DOT Department of Transportation
GHSA Governors’ Highway Safety Association
MPO Metropolitan Planning Organization
PPHH Persons Per Household
TAZ Traffic Analysis Zone
VMT Vehicle Miles Traveled
1
Motivation for Study
Approximately 43,000 people die on the nation’s roads each year. In addition, motor
vehicle crashes are the leading cause of death or injury for persons from age 2 through 33.
These traffic fatality and injury statistics have led to significant interest in highway safety
investments that will save lives.
One relatively unexplored area of research is the setting of safety targets, incentives, or
milestones for jurisdictions. For example, a region may want to achieve a measurable
decrease in pedestrian- involved fatal crashes in a future time period. Using simply the
baseline ( e. g., the current year’s) crash frequencies ( e. g., fatal crashes, injury crashes,
etc.) to set performance targets is inadequate, especially in rapidly developing states such
as Arizona, since the impacts of growth alone will affect the expected safety of a region
or jurisdiction. Specifically, increased vehicle miles traveled ( VMT), increased
population, new drivers, and new facilities will lead to an increase in expected crashes.
Under these circumstances, the current frequency of crashes is not a reliable estimate of
future expected crashes.
Crash prediction models based on statistical or econometric modeling techniques have
been developed for a variety of purposes; most commonly to estimate the expected crash
frequencies from various roadway entities ( highways, intersections, interstates, etc.) and
also to identify geometric, environmental, and operations factors that are associated with
crashes. The vast majority of these models have been developed to forecast crashes on
roadway links and intersections— a scale that is too fine and too cumbersome for
forecasting crashes at the jurisdiction or regional scale.
Agencies, such as departments of transportation ( DOTs) and the Governors’ Highway
Safety Association ( GHSA), may benefit from tools that enable the setting of future
safety targets. These targets may be used to support incentive- based programs within a
jurisdiction— offering incentives based on how many motor- vehicle– related fatalities
( and/ or injuries) are reduced by a region’s safety investment program.
To support an incentive based program, it is necessary to be able to accurately forecast
what safety targets are expected to be in a region or jurisdiction in a future time period,
given changes in road mileage, population, land area, VMT, and so on. This can be
accomplished by estimating crash prediction models using aggregate jurisdiction- level
characteristics as predictors. Of course a defensible and comprehensive set of predictors
must be collected in order to produce a reliable and precise forecasting model.
The purpose of this research is to examine the feasibility of developing a safety
forecasting model in Arizona to support both or either a safety incentive or a safety target
program. A safety incentive program in concept would offer incentives ( e. g., project
funds) for jurisdictions able to show reductions in crashes ( e. g., fatal) due to
implementation of effective safety programs. It is not known whether safety incentive
programs would be adopted or are attractive to jurisdictions or to Metropolitan Planning
Organizations ( MPOs)— but the concept has been raised and discussed in professional
2
forums. It is known, however, that in order to set reasonable safety goals— such as goals
established in a statewide safety management plan— one must be able to forecast the
expected total crashes and fatal crashes within jurisdictions given the planned growth in
population, road mileage, etc. expected over various growth time horizons. Thus, the
need to forecast safety targets has largely been overlooked in Arizona and the U. S. as a
whole.
Motor vehicle crash data along with exposure- related safety data obtained from the U. S.
Census, ADOT, and through questionnaires sent to Arizona jurisdictions were used to
develop the forecasting models and methodology for this project. The models are
intended to enable transportation safety practitioners and decision makers to better
understand the relationship between fatalities and exposure- related safety variables,
especially in jurisdictions with rapid growth, so that future safety targets can be set.
The remainder of this report provides additional background and review of previous
research regarding jurisdiction- level crash forecasting models. The data collected in
support of this research effort are then described. A description of the modeling approach
used in this research is followed by a discussion of modeling results. The procedure to
apply the safety incentive or safety target forecasting model is then given, with two
example applications. Finally, conclusions and recommendations are provided.
3
Background and Relevant Research
The safety profession is replete with models that predict crashes at the microscopic
level— say for intersections or for road segments ( see Bibliography for extensive
examples). These models, however, do not address the forecasting of crashes at more
aggregate levels. Very little research has addressed this issue, and much work is ongoing
in this area of research ( Washington et al. 2006). Other research efforts on aggregate level
forecasting are currently underway at Ryerson Polytechnic University, Purdue University,
and the University of British Columbia. Despite the little research that has been
conducted in this area, much has been learned from prior research on microscopic crash
models.
A reasonable question to ask is: “ Are macroscopic, or jurisdiction- level, statistical models
defensible and logically feasible?” The following arguments, based on accepted
principles and logic from the road safety and statistics communities, support the use of
aggregate level safety prediction models.
1. Crashes are largely random events. Much research has shown that human errors
account for 60% to 90% of crashes. Thus, many crashes are more a function of
human- related factors rather than roadway- related factors. As simple examples,
crashes that result from a driver tuning a radio, answering a cell phone, following
another vehicle too closely, speeding, or running a red light are events that occur
somewhat randomly on a network. It is easy to understand, then, that modeling
crashes at the segment or intersection level is challenging, because there is a large
random component to crashes that is not explained by local road characteristics.
At a more aggregate level, in contrast, crashes are related to aggregate predictors,
such as population demographics, ‘ high risk’ driving populations, the general
classes of road facilities, etc., and assigning crashes to specific links or segments
is not necessary. Thus, by aggregating the transportation system at the Traffic
Analysis Zone( TAZ) 1 level or higher , some of the difficulties caused by
‘ lumpiness’ of random events that we see across intersections or across road
segments are reduced.
2. Aggregate safety differences are substantiated by research. Much research
supports that safety is related to aggregate measures of exposure. First order
effects are revealed as more VMT and crashes, and population and crashes are
strongly and positively correlated. Older drivers suffer from reduced reaction and
perception times, as well as reduced vision and flexibility. Younger drivers suffer
from inexperience and aggressiveness. Minorities have been shown to wear safety
restraints less than whites, and restraint use in rural areas is less than in urban
areas. Interstates have relatively low crash rates, while rural roads with high
speeds have more serious- injury crashes. Crashes in urban areas are attended by
emergency medical services more quickly than crashes in rural areas.
Intersections are locations of complex traffic movements and thus have greater
1 TAZ is the unit of analysis used in metropolitan planning level travel demand models.
4
numbers of crashes than road segments. Increasing traffic congestion tends to
reduce crash severity. School zones are associated with bicycle and pedestrian
crashes. These well supported aggregate relationships, and others not listed here,
are the relationships captured in aggregate level prediction models. The aggregate
relationships described above form the basis for the statistical modeling at the
TAZ level. It is the reliance on these ‘ average’ relationships, and characteristics
measured at the TAZ level, on which model predictions are based.
3. Models for predicting have fewer restrictions than models for explaining.
Intersection and road- segment level accident prediction models are usually held to
a high standard, as they are often used both to predict the expected performance
of such facilities but also to explain relationships between variables. Often, and
sometimes wrongly, these microscopic models are used to infer the effects of
countermeasures, such as the safety effect of the presence of a left- turn lane on
angle crashes. When a model is used simply for prediction, however, and not
inference, there is greater flexibility in model estimation and variable selection
choices. The PLANSAFE model is intended only for prediction, not explanation.
( See Washington et al. 2006 for a discussion of the PLANSAFE model used for
forecasting safety.) Thus, for example, if a population variable is used to predict
fatal crashes per TAZ, its estimated coefficient is used solely in the prediction
equation but is not interpreted to have specific explanatory marginal effects.
These three arguments, or justifications, form the basis for the development of
jurisdiction- level accident prediction models. A consequence of these arguments,
however, is that the models cannot be used for explanation of crash causation or for the
assessment of roadway- specific countermeasures. The aggregate relationships modeled
are suitable for predicting a hypothetical or future outcome should the set of predictors be
changed. This restriction is not too dissimilar from the restriction placed on travel
demand models, whose primary purpose is to predict demand for roadway space of motor
vehicles in hypothetical or future scenarios.
We must also recognize that aggregation reduces the variability and can lead to ecological
correlation, which can lead to interpretation problems. Thus, we must proceed carefully
to examine the forecasting models, to interpret them with caution, and to apply them as
they are intended— to predict future trends in safety given aggregate changes in exposure.
5
Data Collection and Description
Estimating jurisdiction- level crash prediction models to predict safety requires aggregate
information such as socio- economic, demographic, and transportation related data. In
particular, data related to established risk exposure variables are needed.
The analysis unit of this research is the jurisdiction ( cities and towns), since the objective
of this research is to examine how jurisdictional characteristics influence safety. Arizona
consisted of 87 jurisdictions within 15 counties ( as of 2005), which are divided into the
six regional Councils of Governments ( COG) for multi- jurisdictional regional planning as
shown in Figure 1: Central Arizona Association of Governments ( CAAG), Maricopa
Association of Governments ( MAG), Northern Arizona Council of Governments
( NACOG), Pima Association of Governments ( PAG), South Eastern Arizona
Governments Organization ( SEAGO), and Western Arizona Council of Governments
( WACOG). Of course these COG boundaries change over time and currently new COGs
have been formed within the state.
Figure 1: Location of Counties and COGs/ MPOs in Arizona
As mentioned previously, the required input data for the analysis are aggregated by
jurisdiction. The aggregate data came from three sources: crash data, census data, and
through mail surveys. Crash data were collected from the 2000 Arizona Crash Facts
which was published by the Arizona Department of Transportation ( ADOT 2001).
Jurisdiction- level characteristics used for predictors were obtained from Census 2000
data, which includes a variety of socio- demographic information related to people,
business, and geography that is maintained by the U. S. Census Bureau. Since some of the
census data were available only for the year 2000, the number of fatalities that occurred
6
in 2000 was used in the analysis. In addition, the survey response rate was quite
unsatisfactory ( 17 out of 87 surveys were returned, or about 20% response rate, some of
which were incomplete), and so additional variables thought to be important for safety
forecasting were dropped from the analysis. Thus, the analysis is based on results from
2000 crash and census data. The questionnaire sent to jurisdictions is shown in Appendix A.
Jurisdiction- Level Safety Predictors
Although numerous jurisdiction- level safety predictors can be obtained from the U. S.
Census Bureau 2000 data, this research employed nine characteristics for the analysis as
predictors: population change, population density, the percentage of elderly people, the
percentage of young people, the proportion of minorities, the number of dwelling units
per acre, persons per household, number of employees, and mean travel time to work.
Table 1 shows the abbreviated names of the variables and their units of measurement. In
the following section, the characteristics of these nine variables are described in relation
to safety.
VARIABLE DESCRIPTION
PERCHAN The percent change in population from 1990 to 2000
POPDEN Population density ( population/ square mile)
POPELDER Persons aged 65 years old or more as a percentage of the total
population
POPYOUNG Persons aged 17 years old or less as a percentage of the total
population
POPMINOR Total number of minorities as a portion of the total population
HUDEN Number of housing units per square mile
PPHH Persons per household
EMPLOY The number of employees as a percentage of the total population
MTT Mean travel time to work ( minutes), workers age 16+
Table 1: Description and Measurement of Variables Used in the Analysis
Population Change
Crashes are likely to be affected by growth because a jurisdiction is coping with its
growth of infrastructure and population above and beyond what is captured by population
alone. For example, a rapidly growing city is more likely to have new construction
projects, new housing projects, new drivers, business growth, and improvements to the
transportation infrastructure ( upgrading of segments and intersections). These attributes
7
are more likely to be associated with additional crashes compared to a city with no
population growth. The percent change in population was used to capture this effect.
The population of Arizona in 1990 was 3,665,339, while the population in 2000 was
5,130,632, an increase of 40.0% over ten years. Maricopa County had the largest
population in Arizona, but with respect to the percent population change, Mohave County
had the highest as shown in Table 2. In contrast, Greenlee County had the smallest
change in population— a modest 6.7% increase.
County Population
In 1990
Population
In 2000 Change (%)
Mohave County 93,497 155,032 65.8
La Paz County 13,844 19,715 42.4
Yuma County 106,895 160,026 49.7
Pima County 666,957 843,746 26.5
Apache County 61,591 69,423 12.7
Coconino County 96,591 116,320 20.4
Navajo County 77,674 97,470 25.5
Yavapai County 107,714 167,517 55.5
Maricopa County 2,122,101 3,072,149 44.8
Gila County 40,216 51,335 27.6
Pinal County 116,397 179,727 54.4
Cochise County 97,624 117,755 20.6
Graham County 26,554 33,489 26.1
Greenlee County 8,008 8,547 6.7
Santa Cruz County 29,676 38,381 29.3
TOTAL 3,665,339 5,130,632 40.0
Table 2: The Percent Change in Arizona Population from 1990 to 2000 by County
8
As shown in Figure 2, more than 75% of the people in Arizona in 2000 lived in Pima and
Maricopa counties ( 16.45% and 59.88%, respectively). In contrast, 0.17% and 0.38% of
population lived in Greenlee and La Paz counties, respectively. With respect to the
population by jurisdiction, approximately 35% of Arizona residents lived in the cities of
Phoenix and Tucson. Phoenix has the highest population, while Jerome has the smallest
population. The population and percent change by jurisdiction is shown in Appendix B.
Figure 2: Percentage of Total Arizona Population by County in 2000
Population Density
It is reasonable to believe that crashes are more likely to occur in urban areas rather than
rural areas because urban areas have higher accident exposures with regard to Annual
Average Daily Traffic ( AADT) and VMT than rural areas. However, when fatal crashes
are examined the opposite relationship is expected. Rural areas are associated with higher
speeds and generally non- median roadways ( i. e., highways vs. freeways), and thus
crashes tend to be more severe on these facilities. Also, congestion in urban areas tends to
limit speeds, which in turn reduces crash severities. Thus, degree of urbanization should
be negatively associated with fatal crashes and positively associated with total crashes.
The population density of a jurisdiction is calculated by dividing the population by land
area of the jurisdiction.
9
Arizona covers 114,006 square miles ( 113,642 square miles of land areas and 364 square
miles of water areas), making it the sixth largest of the 50 states. Despite the vast area,
Arizona has a relatively small number of counties ( 15). Coconino is the largest county
( 18,617.4 square miles); Santa Cruz is the smallest ( 1,237.6 square miles). Table 3 ( p. 8)
shows the counties’ land areas. .
Councils of Governments County Land Area
Mohave County 13,311.6
WACOG La Paz County 4,500.0
Yuma County 5,514.1
PAG Pima County 9,186.3
Apache County 11,204.9
Coconino County 18,617.4
Navajo County 9,953.2
NACOG
Yavapai County 8,123.3
MAG Maricopa County 9,203.1
Gila County 4,767.7
CAAG
Pinal County 5,369.6
Cochise County 6,169.4
Graham County 4,629.3
Greenlee County 1,847.0
SEAGO
Santa Cruz County 1,237.6
TOTAL 113,634.6
Table 3: Arizona Land Areas by County in 2000
10
The average population density of Arizona in 2000 was 45.2 persons per square mile.
Maricopa County had the highest of the 15 counties ( 333.8/ mi2), whereas La Paz County
had the lowest ( 4.4/ mi2) Table 4 shows the population density of all the counties. In terms
of population density by city, Guadalupe had the highest density ( 6,813.9), while
Buckeye had the lowest density ( 44.8). Population densities by jurisdiction— the unit of
analysis used for modeling— are summarized in Appendix C.
County Land Area Population Population
Density
Mohave County 13,311.6 155,032 11.6
La Paz County 4,500.0 19,715 4.4
Yuma County 5,514.1 160,026 29.0
Pima County 9,186.3 843,746 91.8
Apache County 11,204.9 69,423 6.2
Coconino County 18,617.4 116,320 6.2
Navajo County 9,953.2 97,470 9.8
Yavapai County 8,123.3 167,517 20.6
Maricopa County 9,203.1 3,072,149 333.8
Gila County 4,767.7 51,335 10.8
Pinal County 5,369.6 179,727 33.5
Cochise County 6,169.4 117,755 19.1
Graham County 4,629.3 33,489 7.2
Greenlee County 1,847.0 8,547 4.6
Santa Cruz County 1,237.6 38,381 31.0
TOTAL 113,634.6 5,130,632 45.2
Table 4: Arizona Population Densities by County in 2000
11
The Percentage of Elderly and Young Populations
The percentages of elderly and young people are factors that are related to crashes, as
mentioned previously. Young drivers are generally inexperienced, while elderly drivers
suffer from reduced perception and reaction times as well as crash survivability. A total of
667,839 people, about 13.0% of the population, were 65 years old or more in Arizona in
2000. A total of 1,150,466 people, about 22.4% of the population, were 17 years old or
less in 2000. Of the 15 counties, Maricopa County had the highest number of both elderly
and young people, and with respect to jurisdictions, Phoenix had the highest number of
both elderly and young people.
Besides these age- related factors, this research employs the proportion of minorities as a
predictor of severe crashes. Minorities, on average, wear safety restraints less than whites
( see White et al. 2001 and Washington et al. 1999) and tend to drive older vehicles with
less extensive safety features ( compared to new vehicles). Phoenix was found to have the
highest number of minorities. Table 5 shows the number of elderly, young, and minorities
by county.
County Elderly People Young People Minority
Mohave County 20,801 19,063 15,786
La Paz County 2,139 977 1,967
Yuma County 12,388 26,681 62,785
Pima County 66,911 111,925 236,186
Apache County 1,002 2,555 2,488
Coconino County 3,689 13,239 19,779
Navajo County 3,798 8,791 11,318
Yavapai County 22,056 16,699 14,401
Maricopa County 276,354 672,338 1,000,267
Gila County 5,664 4,657 6,289
Pinal County 16,017 19,974 42,397
Cochise County 10,191 15,538 31,654
Graham County 2,327 3,740 5,410
Greenlee County 371 922 1,824
Santa Cruz County 2,448 6,159 20,105
TOTAL 667,839 1,150,466 1,856,374
Table 5: Arizona Population of Elderly, Young, and Minorities by County in 2000
12
Residential Dwelling Density and Persons per Household
Residential dwelling density ( the number of housing units per square mile) and persons
per household were also used as predictors to model jurisdiction- level crash prediction
models ( see Table 6). Residential dwelling density is a surrogate for the compactness of
development— which corresponds to high intersection intensity ( the questionnaire in
Appendix A tried to capture this more explicitly). Persons per household might reflect
socio- economic status, which may correlate with vehicle age and safety equipment,
employment, etc. The total number of housing units over 87 jurisdictions within 15
counties was 1,660,557. Of the 15 counties, Maricopa County and La Paz County had the
highest and smallest house densities, respectively. With respect to residential density by
jurisdiction, South Tucson was the highest ( 2,059.0) whereas Buckeye was the lowest
( 16.1).
The number of persons per household ( PPHH) for the 87 Arizona jurisdictions ranged
from 1.74 ( Youngtown) to 7.51 ( Colorado City), while the average number of persons per
household was 2.79. Unlike residential density, Colorado City was found to have the
highest and Youngtown the lowest persons per household respectively.
County Number of
Housing Units
Housing Density Average Number
of PPHH
Mohave County 50,509 1,273.4 2.45
La Paz County 4,343 140.4 2.32
Yuma County 40,911 2,419.7 2.86
Pima County 232,563 3,734.6 2.47
Apache County 4,001 440.4 3.41
Coconino County 25,661 582.6 2.80
Navajo County 14,768 874.8 3.17
Yavapai County 45,725 2,267.8 2.33
Maricopa County 1,139,705 14,507.4 2.67
Gila County 11,663 2,001.0 2.50
Pinal County 46,014 3,682.0 2.68
Cochise County 30,344 2,272.2 2.55
Graham County 5,880 1,089.0 2.99
Greenlee County 1,471 220.6 2.73
Santa Cruz County 6,999 727.5 3.23
TOTAL 1,660,557 36,233.4 2.79
Table 6: Arizona Number of Housing Units, Density, and Persons per Household
by County in 2000
13
Number of Employees and Mean Travel Time to Work
Relatively large numbers of employees lead to an increase in the number of trips, which
increases traffic volume, and the increased trips and traffic volume may also increase
exposure to the risk of motor- vehicle- related crashes. Also, work trips tend to include
aggressive and/ or distracted drivers. Consequently, the higher number of employees
might be highly correlated with the higher crash frequencies. Due to the potential
correlation between the number of employees and crash frequencies, the number of
employees was included as an independent variable.
Similarly, crash frequencies might be expected to increase as mean travel time to work
grows because the longer travel times suggest higher exposure levels and greater levels of
driver fatigue. The mean travel time to work in Arizona is 22.1 minutes, as shown in Table 7.
County Number of Employees Mean Travel Time to Work
( minutes)
Mohave County 78,758 20.6
La Paz County 5,453 17.2
Yuma County 73,596 18.6
Pima County 420,263 23.9
Apache County 6,600 28.0
Coconino County 49,627 19.0
Navajo County 23,894 22.9
Yavapai County 80,491 22.5
Maricopa County 2,148,360 26.1
Gila County 19,535 20.3
Pinal County 77,672 27.4
Cochise County 53,114 19.8
Graham County 11,276 22.6
Greenlee County 2,421 20.3
Santa Cruz County 14,982 19.7
TOTAL 3,006,042 22.1
Table 7: Arizona Number of Employees and Mean Travel Time to Work
by County in 2000
Jurisdiction- Level Crash Data
As mentioned previously, crash data used in this research were obtained from the 2000
Arizona Crash Facts. In that year, 131,368 crashes and 891 fatal crashes occurred in Ari-zona.
Excluding crashes that occurred within a specific county but not within a specific
city ( e. g., state rural roads in Apache County experienced 358 total crashes and 10 fatal
crashes in 2000), 108,176 total crashes and 392 fatal crashes occurred in the 87 Arizona
jurisdictions ( cities or towns). Of the 87 jurisdictions, the City of Phoenix had the greatest
14
number of total crashes and fatal crashes, with 44,146 crashes and 168 fatal crashes
reported. Zero crashes were reported in eight jurisdictions, whereas a total of 47 juris-dictions
reported zero fatal crashes in 2000. Table 8 presents the frequency of total crashes
and fatalities across the 87 Arizona jurisdictions in 2000 ( excluding crashes occurring on
state rural roads or other rural roads outside a jurisdiction but within the county).
As shown in table 8, crash frequencies by jurisdiction for fatal crashes are quite small
relative to total crashes. As a result, statistical models based on total crashes will tend to
be more reliable than those on fatal crash data. Also of note is the preponderance of
zeroes reported in the fatal crash column. A large number of zeroes is a common
phenomenon with fatal crash data across analysis units. These zeroes tend to raise
challenges in the estimation of statistical models, as described by Lord et al. ( 2004). In
the analysis that follows we generally follow the advice of Lord et al. ( 2004) in dealing
with the ‘ excess’ zeroes.
County Jurisdiction Total Crashes Fatal Crashes
Cochise County Benson 36 0
Bisbee 48 1
Douglas 321 1
Huachuca City 7 1
Sierra Vista 775 2
Tombstone 19 0
Willcox 39 0
Graham County Pima 14 0
Safford 113 0
Thatcher 48 0
Greenlee County Clifton 30 0
Duncan 0 0
Santa Cruz County Nogales 411 1
Patagonia 0 0
TOTAL 1,861 6
Mohave County Bullhead City 673 4
Colorado City 17 0
Kingman 400 1
Lake Havasu City 525 6
La Paz County Parker 16 0
Quartzsite 38 0
Yuma County San Luis 0 0
Somerton 16 0
Wellton 1 0
Yuma 1,489 3
TOTAL 3,175 14
Table 8 Arizona Total and Fatal Crashes by Jurisdiction in 2000
15
County Jurisdiction Total Crashes Fatal Crashes
Pima County Marana 545 1
Oro Valley 263 2
Sahuarita 40 0
South Tucson 181 0
Tucson 14,822 52
TOTAL 15,851 55
Apache County Eagar 44 0
Saint Johns 25 0
Springerville 1 0
Coconino County Flagstaff 2,480 7
Fredonia 3 0
Page 123 2
Williams 53 2
Navajo County Holbrook 83 1
Pinetop- Lakeside 96 0
Show Low 133 0
Snowflake 80 1
Taylor 6 0
Winslow 162 1
Yavapai County Camp Verde 89 0
Chino Valley 83 3
Clarkdale 0 0
Cottonwood 196 1
Jerome 10 0
Prescott 883 2
Prescott Valley 357 2
Sedona 0 0
TOTAL 4,907 22
Maricopa County Avondale 473 0
Buckeye 6 2
Carefree 9 0
Cave Creek 10 0
Chandler 3,056 4
El Mirage 114 3
Fountain Hills 69 0
Gila Bend 18 0
Gilbert 1,352 7
Glendale 4,997 27
Goodyear 249 4
Table 8 continued
16
County Jurisdiction Total Crashes Fatal Crashes
Maricopa County Guadalupe 35 0
( continued) Litchfield Park 0 0
Mesa 11,019 30
Paradise Valley 239 0
Peoria 1,554 1
Phoenix 44,146 168
Queen Creek 0 0
Scottsdale 4,555 19
Surprise 244 3
Tempe 8,453 16
Tolleson 125 0
Wickenburg 97 2
Youngtown 0 0
TOTAL 80,820 286
Gila County Globe 141 0
Hayden 5 1
Miami 24 0
Payson 139 0
Winkelman 2 0
Pinal County Apache Junction 331 3
Casa Grande 661 2
Coolidge 82 0
Eloy 83 2
Florence 60 1
Kearny 4 0
Mammoth 9 0
Superior 21 0
TOTAL 1,562 9
Table 8 continued
17
Methodological Approach and Modeling Results
Methodological Approach
Two different approaches are generally used to estimate crash predictions, Poisson
regression and negative binomial regression ( Jovanis and Chang 1986; Washington et al.
2003), although various other modeling approaches are possible ( see for example Lord et
al. 2004). Crash counts are approximated well by a Poisson process ( Joshua and Garber
1990), since crash counts are discrete, positive integers. The Poisson regression model
requires that the variance of the crash frequency is approximately equal to its mean. In
much of the observed crash data, however, the variance of the crash frequency is greater
than the mean and overdispersion occurs ( Miaou et al. 1992). Miaou et al. introduced the
negative binomial distribution for modeling traffic safety which accommodates greater
variance in the data than allowed by the Poisson distribution. The overdispersion
typically arises from variation in crash means across sites. As a result, the negative
binomial regression model is the preferred modeling approach when overdispersion is
present ( Washington et al. 2003). This research employs the negative binomial regression
model to develop jurisdiction- level crash prediction models. The negative binomial
regression model is briefly summarized in the following section.
The Negative Binomial regression model specifies a relationship between the expected
number of crashes occurring at the ith element and the q parameters, Xi1, Xi2, …, Xiq, as
follows:
( ) exp( ) i i 0 1 i1 2 i2 q iq i E y = μ = β + β X + β X + 􀀢 􀀢 + β X + ε
In addition, the Negative Binomial regression model includes a quadratic term in the
variance to reflect overdispersion in the model variance. As a result, the Negative
Binomial regression model takes the following form:
μ α
μ
α
α
− + +
+ −
=
i
i
y
y
i
i
i y
P y y
!( 1)! ( 1 )
() ( 1)! ,
where α is the overdispersion parameter and the variance is:
( ) ( ) 2 i i i Var y = μ + α μ .
The overdispersion or extra- Poisson variation is generally due to variables omitted from
the model that explain variation in crashes between sites. If α is equal to 0, the Negative
Binomial reduces to a Poisson model. The value of α corresponds with the degree of
overdispersion over and above that associated with the mean i μ
.
Similar to previous studies, the final model structure used is
( ) exp i jij Ey = Σβx
where ( ) i E y is the expected number for jurisdiction i, ij x ’ s are variables describing
safety- related exposure variables for jurisdictions, and the βj are estimated parameters or
effects of the predictor variables.
Modeling Results
First, we examined the correlation between independent variables, since one of the
problems with multiple regression is that explanatory variables may be correlated, thus
confounding the effects of variables with one another. In particular, regression
coefficients that indicate the effect of one factor may change when some other factor is
added or removed from the model.
Figure 3 shows the correlation between independent variables used in the study. Using
statistical tests of significant correlation, it was found that the percentage of young people
( POPYOUNG) and persons per household ( PPHH) are highly positively correlated with
ρ = 0.8545, whereas the percentage of young people ( POPYOUNG) and the number of
employees ( EMPLOY) are highly negatively correlated with ρ =- 0.972.
Correlation Matrix
perchan popden popelder popyoung popminor huden pphh emppop mtt
perchan 1.0000
popden 0.0610 1.0000
popelder 0.0093 - 0.1262 1.0000
popyoung - 0.0863 0.1185 - 0.7084 1.0000
popminor - 0.1699 0.3595 - 0.4187 0.4282 1.0000
huden - 0.0940 0.7464 - 0.0131 - 0.0360 0.2525 1.0000
pphh - 0.0071 0.1794 - 0.5845 0.8545 0.3720 - 0.0172 1.0000
emppop 0.0986 - 0.1061 0.7401 - 0.9720 - 0.4379 0.0433 - 0.8188 1.0000
mtt 0.4228 0.1901 - 0.0255 0.0895 - 0.0534 0.1674 0.1382 - 0.0653 1.0000
Figure 3: Correlation Matrix of Predictor Variables
The explanatory variables described in Table 1 were used in the software program
LIMDEP ( copyright William Greene) to choose the significant variables for the
jurisdiction- level fatal crash model. One of the disadvantages with the LIMDEP software
is that the LIMDEP does not automate the process of removing insignificant variables
from the model, one at a time, until only significant variables are left in the model. Thus,
various models were tested to estimate the possible nature of the relationships between
the independent variables and fatal crashes, beginning with a ‘ full’ model with many
variables. Table 9 presents the estimation results for a fatal crash model with a ‘ full’
( complete) set of predictor variables.
18
19
Among the 9 variables, only five variables were found to be statistically significant at the
10% significance level ( shown in bold): PERCHAN, POPDEN, POPELDER, HUDEN,
and PPHH. These variables, therefore, serve as predictors of fatal crashes. Two
statistically significant variables, PERCHAN and HUDEN, are positively associated with
fatal crashes, while the other three variables are negatively related with fatal crashes.
Variable Coefficient Standard Error t- statistics p- value
Constant 2.4299 17.345 0.140 0.889
PERCHAN 0.0082 0.004 2.054 0.040
POPDEN - 0.0004 0.000 - 1.885 0.059
POPELDER - 0.1258 0.041 - 3.033 0.002
POPYOUNG 0.1141 0.202 0.565 0.572
POPMINOR 0.0009 0.014 0.067 0.947
HUDEN 0.0033 0.001 4.782 0.000
PPHH - 2.5289 1.224 - 2.066 0.039
EMPLOY 0.0428 0.174 0.247 0.805
MTT - 0.0258 0.046 - 0.564 0.573
α ( overdispersion parameter) 1.9937 0.513 3.886 0.000
Number of observations
Log- likelihood at zero
Log- likelihood at convergence
87
- 385.4672
- 143.3673
Table 9: Negative Binomial Model Estimation Results of Fatal Crashes with
Complete Set of Predictors
20
Table 10 shows the results of three new models retaining significant predictor variables for
fatal crashes by jurisdiction in Arizona. The table also compares these models to previously
reported and aggregate fatal crash models estimated through other research efforts. It should
be noted that the effort by Van Schalkwyk et al. in 2006 used Traffic Analysis Zones ( TAZ)
as the unit of analysis, and not jurisdiction. With that said, however, the explanatory power
of the Van Schalkwyk model is 75% compared to about 15% for the ‘ best’ model developed
in this effort ( Model 3).
Fatal Crash Models
Existing Models New Models
Variable De Guevara
et al. 2004
Van Schalkwyk
et al. 2006
Model 1 Model 2 Model 3
Constant 0.652 0.017 7.7549 6.49361
POPDEN 0.050782 - 0.0006 - 0.0004
POPMINOR - 5.18194 0.319
INTDEN - 4.81647 - 0.0924
PERCHAN 0.005736 0.004494 0.006366
HUDEN 0.003984 0.002577 0.003154
POPELDER - 0.16036 - 0.13637
PPHH - 2.30763 - 1.96688
PNF_ 0111* 1.762
PNF_ 0512** 1.389
POP00_ 15*** 0.000263
Log-likelihood
- 394.882 N/ A - 149.847 - 145.369 - 143.801
Pseudo R2 N/ A 0.75 0.1147 0.1412 0.1504
* PNF_ 0111 = Proportion ( of total road mileage) of urban and rural interstates in jurisdiction; ** PNF_ 0512 = Proportion of freeways
and expressways in jurisdiction; *** POP00_ 15 = Population aged 0 to 15 years old in jurisdiction.
Table 10: Three New Fatal Crash Models and Comparison to Previously
Estimated Models
This result is partially explained by the fact that variability is lost with increasing levels of
aggregation, and thus the ability to explain variability is also lost. Jurisdictions are cer-tainly
more aggregated than Traffic Analysis Zones. The second important reason is that
the questionnaire administered as part of this research aimed to capture many of the impor-tant
variables that were thought to help explain variation in safety risk across jurisdictions.
Because of the poor overall response rate, and incomplete surveys among those who did
respond, the opportunity to capture additional explanatory variables was missed. As is the
case for most surveys, response rates are directly proportional to the ease of providing the
information, the motivation of the respondent, the frequency of follow- ups, and the ability
for the survey team to assist when possible. Improving response rates for future surveys of
this type would require additional resources to enable these critical elements.
21
Procedure to Apply the Safety Incentive or Safety Target
Forecasting Model
Model 3 shown in Table 10 can be used to predict fatal crashes; however, the precision of
this model is quite low. In other words, for any given set of predictors, there is a large
amount of unexplained variability in the number of fatal crashes occurring within a
jurisdiction. Regardless of the questionable precision of the model, the following
procedure reveals how safety forecasting is performed with this or a similar model.
1. Collect variables needed to run models: All model variables need to be collected for
the jurisdiction being analyzed. The five variables needed to forecast fatal crashes include
POPDEN, PERCHAN, HUDEN, POPELDER, and PPHH ( see Table 1 for a description
and measurement units of these predictor variables).
2. Generate the expected crash counts in a spreadsheet program ( such as Microsoft
Excel) or database management software program ( such as Microsoft Access): The
simple equation derived from the logarithmic negative binomial regression model
estimation results presented in the previous section is used to calculate the expected fatal
crash count ( e. g., pedestrian, total, fatal, etc.) by jurisdiction in the base year and the
incentive year ( e. g., an incentive is given if the jurisdiction meets safety targets in two
years). The model predicts the expected ( mean for all jurisdictions with these predictors)
count of fatal crashes expected per year.
A spreadsheet model can be simply set up in Excel that uses the negative binomial
prediction equation, E( yi)= exp Σβjxij , and the estimated coefficients shown for
Model 3 in Table 10.
Table 11 shows a spreadsheet developed in Microsoft Excel for Model 3 using a
hypothetical jurisdiction in the Base year and after years 1 and 2. Shown in the table are
the values of the predictor variables, reflecting growth and change in the predictor
variables expected during a two year time horizon. For example, the 10- year population
growth rate is expected to increase from 55% to 59% by year 2. Population density is
expected to increase from the base year of 150 to 160 persons per square mile.
Predictor Values
Coefficient Jurisdiction A: Base Jurisdiction A: Year 1 Jurisdiction A: Year 2
constant 6.49361 n/ a n/ a n/ a
POPDEN - 0.0004 150 155 160
POPCHANGE 0.006366 55 57 59
HUDEN 0.003154 150 150 150
POPELDER - 0.13637 10 12 14
PPHH - 1.96688 2 2.05 2.1
Fatal Crash Prediction 7.09 4.95 3.45
Table 11: Example 1: Excel Prediction Spreadsheet for Fatal Crash
Prediction Model
22
In example 1 ( Table 11), the predicted number of fatal crashes is expected to decrease
from 7.09 to 3.45 crashes in year 2. Thus, without any safety investments, fatal crashes in
Jurisdiction A will be reduced by approximately 3.5 fatal crashes. Safety targets for this
jurisdiction should be set appropriately to account for the natural reduction in fatal
crashes.
Example 2, shown in Table 12, shows Jurisdiction B growing rapidly. Its elderly
population is expected to decrease by 2% over the next 2 years, while the 10- year growth
rate is expected to increase by 25%. In the base year 14.46 fatal crashes are expected,
while in year 2, 22.27 fatal crashes are expected. Thus, approximately 7 additional fatal
crashes are expected in Jurisdiction B based on growth trends alone. In this case a safety
target to maintain 14 crashes in year 2 would be extremely aggressive and would require
a significant safety investment.
Predictor Values
Coefficient Jurisdiction B: Base Jurisdiction B: Year 1 Jurisdiction B: Year 2
constant 6.49361 n/ a n/ a n/ a
POPDEN - 0.0004 75 75 75
POPCHANGE 0.006366 55 65 80
HUDEN 0.003154 150 150 150
POPELDER - 0.13637 5 4 3
PPHH - 1.96688 2 2 2
Fatal Crash Prediction 14.46 17.66 22.27
Table 12: Example 2: Excel Prediction Spreadsheet for Fatal Crash
Prediction Model
3. Incorporate modeling results into incentive program: The modeling results in Table
11 predict that fatal crashes will decrease as a result of projected growth in the
jurisdiction and without any safety investments. Thus, safety investments should be
expected to improve safety above and beyond that expected from growth alone and be the
result of effective safety investments. Thus, Jurisdiction A might be expected to show a
reduction in fatal crashes to less than expected, say one or two crashes, while Jurisdiction
B ( Table 12) might be allowed to show an increase of three crashes over the base year.
The structuring of any incentive program, of course, would be devised in the state and
administered by the appropriate agencies and/ or stakeholders.
4. Calibration to Local Conditions: With an improved model ( not one with low
explanatory power), a calibration procedure will be conducted to translate the expected
reduction/ increase in crashes to the observed counts of crashes in a jurisdiction. This
calibration procedure will be developed along with improved models in the future.
23
Conclusions and Recommendations
The data used in this research were obtained from ADOT and the U. S. Census Bureau,
and were compiled for the year 2000. A significant effort was undertaken to collect a host
of additional and important explanatory variables to improve the safety prediction model
( see Appendix A), by mailing a survey to all jurisdiction representatives in Arizona.
Many important exposure- related variables, such as road mileage by functional class,
number and type of schools, number of intersections ( signalized or stop- controlled), and
weather- related variables were sought via the survey and were ultimately unavailable.
This set of additional variables represents important predictors of safety, and fatal crashes
in particular. Unfortunately, the lack of a complete set of predictors undermined the
modeling effort.
The statistical modeling results reflect the exclusion of important variables and will lead
to imprecise predictions of fatal crash frequencies. As shown in Table 10, the ‘ best’ model
in this effort produced a model with an R- Square value of approximately 15% –
suggesting that 15% of the variation in fatal crashes across jurisdictions in Arizona is
explained by the set of predictors in the model. Initial efforts in NCHRP 8- 44 ( by the
same authors of this report) have produced similar models with explanatory power above
75%. These models have included many of the predictors sought in the questionnaire
shown in Appendix A and also shown in Table 13.
While this report provides an analytical procedure for predicting fatal crash frequencies
using a predictive model ( see Table 11 and Table 12), its use is not recommended due to
lack of explanatory power and precision of the model. These model deficiencies lead to
the following problems:
1. The variability across jurisdictions with a similar set of predictor values will be
large. Thus, the predicted fatal crash frequency will represent the mean value of
a highly dispersed distribution of values.
2. Problem 1 above leads to a dilemma of dealing with the dispersion not explained
by the model. A Bayesian correction of sorts, for example, could be used if
known important variables were not missing; however, a Bayesian correction is
problematic in the absence of known important explanatory variables.
3. When an observed fatal crash count in a jurisdiction is not close to the predicted
fatal crash count in the base year a remedy is not known. The difference could be
due to safety deficiencies, due to omitted important predictor variables, or due to
mostly random and unknown effects. The missing important predictor variables
need to be minimized.
4. Problems of omitted variables— well known to the econometrics community—
will bias model predictions ( see Kim et al. 2006a and 2006b and Washington et
al. 2003).
The recommendation is to supplement this report with NCHRP 8- 44- 2 findings when
they become available in April of 2009. The objectives of this NCHRP project— led by
Dr. Simon Washington— are nearly the same as those of this research effort except that
24
the NCHRP project is for a national audience. The objectives of this NCRHP research,
and the similarity to this ADOT project, can be seen at
http:// www. trb. org/ TRBNet/ ProjectDisplay. asp? ProjectID= 919.
It is anticipated that a more complete set of predictors, currently being developed for
NCHRP 8- 44- 2 for Pima and Maricopa counties in Arizona, will yield a more precise and
reliable model for the purpose of devising safety incentives— at least for all jurisdictions
in the MAG and PAG regions. Table 13 shows a sample of some of the predictor
variables that will be available in project 8- 44- 2. Compared to the data available in this
effort, the current effort does not have variables related to weather, to high- risk non-motorized
populations, to speeds and design standards, or to conflicts. Again, the intent
was to capture many of these variables through the questionnaire administered as part of
this project, but poor response rates resulted in a genuine lack of useful data which lead
to the inability to estimate precise forecasting models.
Major Contributing Factor Potential Aggregate ( TAZ level) Variables that may capture
effect of Major Factor ( assumes time scale is year)
Weather Proportion of wet pavement days per year
Proportion of icy pavement days per year
Proportion of snow days per year
Proportion of fog/ reduced visibility days per year
Proportion of sunny days per year
High risk driving populations
Population/ number of licensed drivers
Proportion of population between 16 and 24
Proportion of population over 60
Number of DUI arrests
Employed/ unemployed workers
High risk non motorized
populations
Number of crosswalks
Number of schools ( elementary, middle, high, college)
Percentage/ mileage of sidewalks ( of street mileage)
Percentage/ mileage of bicycle facilities
Speed, design standards of
facilities, and access control
Total street mileage
Proportion of local road mileage
Proportion of collector road mileage
Proportion of arterial road mileage
Proportion of rural highway mileage ( urban/ rural)
Proportion of interstate ( urban and rural)
Conflicts Number/ proportion of signalized intersections
Number/ proportion of stop- controlled intersections
Intersection density
Total area
Table 13: Description of Important Predictor Variables for Safety
Forecasting Model
It is anticipated that NCHRP 8- 44- 2 will produce statistical models with superior pre-dictive
ability and for numerous safety outcomes in addition to fatal crashes. For example,
in addition to fatal crash models, it is anticipated that 8- 44- 2 will produce statistical
models able to forecast total accidents, property damage accidents, incapacitating injury
and fatal crashes, night- time crashes, pedestrian crashes, injury crashes, and bicycle-related
crashes. Thus, an incentive or target program that sets targets across a broad range
of crash outcomes, not just fatal crashes, could be supported with such models.
25
Finally, while the goals and objectives are quite complementary, it is important to note
that the NCHRP 8- 44- 2 effort will not result in the ability to forecast crash outcomes
outside of the MAG and PAG regions. Thus, a safety incentive or target program cannot
be supported statewide, but instead only in these two major regions.
To support a statewide safety incentive or safety target program, the data needed to
estimate these models would need to be made available and/ or collected. Data collection
efforts would be needed in jurisdictions throughout the state including tribes, counties,
and townships.
26
27
Appendix A: Questionnaire Sent to Jurisdictions
Thank you for taking the time to complete the following survey. The information you provide will be used to
help us develop fatality crash models to predict a fair and reasonable fatality rate for each jurisdiction. Please
note that the information you provide should be based on the year of 2000.
1. Your city or town name:
2. Road mileage information by road functional classification:
􀁹 Total mileage of all functional classes of roads:
􀁹 Total mileage of principal arterial interstate:
􀁹 Total mileage of principal arterial expressway:
􀁹 Total mileage of principal arterial:
􀁹 Total mileage of minor arterial:
􀁹 Total mileage of major collector rural:
􀁹 Total mileage of minor collector rural:
􀁹 Total mileage of urban collector:
􀁹 Total mileage of local streets:
3. School information
􀁹 Number of elementary schools:
􀁹 Number of middle schools:
􀁹 Number of high schools:
4. How many intersections and bus stops were there within your city ( or town) in 2000?
􀁹 Intersections: 􀁹 Bus stops:
5. How many people had driver licenses in 2000?
6. How many tickets were issued in 2000?
7. How many tickets related to speeding were issued in 2000?
8. How many DUI related accidents occurred in 2000?
9. Weather information:
􀁹 What is the annual average precipitation in 2000? inches
􀁹 What is the annual average snowfall in 2000? inches
Please return this survey by November 10th by fax on 480- 965- 0557 ( Do- Gyeong Kim) or via email at
dokkang@ u. arizona. edu.
28
Appendix B: Arizona Population and Population Change
Statistics by Jurisdiction ( 2000)
Jurisdictions Population in
1990
Population in
2000 Change (%)
Bullhead City 21,951 33,769 53.8
Colorado City 2,426 3,334 37.4
Kingman 12,722 20,069 57.8
Mohave County
Lake Havasu City 24,363 41,938 72.1
La Paz County Parker 2,897 3,140 8.4
Quartzsite 1,876 3,354 78.8
San Luis 4,212 15,322 263.8
Somerton 5,282 7,266 37.6
Wellton 1,066 1,829 71.6
Yuma County
Yuma 56,966 77,515 36.1
Marana 2,187 13,556 519.8
Oro Valley 6,670 29,700 345.3
Sahuarita 1,629 3,242 99.0
South Tucson 5,171 5,490 6.2
Pima County
Tucson 405,371 486,699 20.1
Eagar 4,025 4,033 0.2
Saint Johns 3,294 3,269 - 0.8
Apache County
Springerville 1,802 1,972 9.4
Flagstaff 45,857 52,894 15.3
Fredonia 1,207 1,036 - 14.2
Page 6,598 6,809 3.2
Coconino County
Williams 2,532 2,842 12.2
Holbrook 4,686 4,917 4.9
Pinetop- Lakeside 2,422 3,582 47.9
Show Low 5,020 7,695 53.3
Snowflake 3,679 4,460 21.2
Taylor 2,418 3,176 31.3
Navajo County
Winslow 9,279 9,520 2.6
Camp Verde 6,243 9,451 51.4
Chino Valley 4,837 7,835 62.0
Clarkdale 2,144 3,422 59.6
Cottonwood 5,918 9,179 55.1
Jerome 403 329 - 18.4
Prescott 26,592 33,938 27.6
Prescott Valley 8,904 23,535 164.3
Yavapai County
Sedona 7,720 10,192 32.0
29
Jurisdictions Population in
1990
Population in
2000 Change (%)
Maricopa County Avondale 16,169 35,883 121.9
Buckeye 4,436 6,537 47.4
Carefree 1,657 2,927 76.6
Cave Creek 2,925 3,728 27.5
Chandler 89,862 176,581 96.5
El Mirage 5,001 7,609 52.1
Fountain Hills 10,030 20,235 101.7
Gila Bend 1,747 1,980 13.3
Gilbert 29,122 109,697 276.7
Glendale 147,864 218,812 48.0
Goodyear 6,258 18,911 202.2
Guadalupe 5,458 5,228 - 4.2
Litchfield Park 3,303 3,810 15.3
Mesa 288,104 396,375 37.6
Paradise Valley 11,773 13,664 16.1
Peoria 50,675 108,364 113.8
Phoenix 983,392 1,321,045 34.3
Queen Creek 2,667 4,316 61.8
Scottsdale 130,075 202,705 55.8
Surprise 7,122 30,848 333.1
Tempe 141,993 158,625 11.7
Tolleson 4,434 4,974 12.2
Wickenburg 4,515 5,082 12.6
Youngtown 2,542 3,010 18.4
Gila County Globe 6,062 7,486 23.5
Hayden 909 892 - 1.9
Miami 2,018 1,936 - 4.1
Payson 8,377 13,620 62.6
Winkelman 676 443 - 34.5
Pinal County Apache Junction 18,092 31,814 75.8
Casa Grande 19,076 25,224 32.2
Coolidge 6,934 7,786 12.3
Eloy 7,211 10,375 43.9
Florence 7,321 17,054 132.9
Kearny 2,262 2,249 - 0.6
Mammoth 1,845 1,762 - 4.5
Superior 3,468 3,254 - 6.2
30
Jurisdictions Population in
1990
Population in
2000 Change (%)
Cochise County Benson 3,824 4,711 23.2
Bisbee 6,288 6,090 - 3.1
Douglas 13,137 14,312 8.9
Huachuca City 1,782 1,751 - 1.7
Sierra Vista 32,983 37,775 14.5
Tombstone 1,220 1,504 23.3
Willcox 3,122 3,733 19.6
Graham County Pima 1,725 1,989 15.3
Safford 7,359 9,232 25.5
Thatcher 3,763 4,022 6.9
Greenlee County Clifton 2,840 2,596 - 8.6
Duncan 662 812 22.7
Santa Cruz County Nogales 19,489 20,878 7.1
Patagonia 888 881 - 0.8
31
Appendix C: Arizona Population Density by Jurisdiction ( 2000)
Jurisdiction Land Area Population Population
Density
Bullhead City 45.2 33,769 746.6
Colorado City 10.5 3,334 317.3
Kingman 30.0 20,069 669.7
Mohave County
Lake Havasu City 43.0 41,938 974.4
La Paz County Parker 22.0 3,140 142.8
Quartzsite 36.3 3,354 92.4
San Luis 26.4 15,322 579.5
Somerton 1.3 7,266 5,483.2
Wellton 2.5 1,829 727.3
Yuma County
Yuma 106.7 77,515 726.8
Marana 72.7 13,556 186.6
Oro Valley 31.8 29,700 933.1
Sahuarita 15.2 3,242 213.2
South Tucson 1.0 5,490 5,446.6
Pima County
Tucson 194.7 486,699 2,500.1
Eagar 11.3 4,033 355.6
Saint Johns 6.6 3,269 494.8
Apache County
Springerville 11.5 1,972 170.8
Flagstaff 63.6 52,894 831.9
Fredonia 7.4 1,036 139.7
Page 16.6 6,809 410.5
Coconino County
Williams 43.5 2,842 65.3
Holbrook 15.4 4,917 318.4
Pinetop- Lakeside 11.3 3,582 318.1
Show Low 27.9 7,695 276.2
Snowflake 30.8 4,460 144.8
Taylor 24.6 3,176 129.1
Navajo County
Winslow 12.3 9,520 773.1
Camp Verde 42.6 9,451 222.0
Chino Valley 18.6 7,835 421.6
Clarkdale 7.3 3,422 466.9
Cottonwood 10.7 9,179 860.3
Jerome 0.7 329 462.1
Prescott 37.1 33,938 915.6
Prescott Valley 31.7 23,535 742.0
Yavapai County
Sedona 18.6 10,192 548.0
32
Jurisdiction Land Area Population Population
Density
Maricopa County Avondale 41.3 35,883 869.7
Buckeye 145.8 6,537 44.8
Carefree 8.8 2,927 330.8
Cave Creek 28.2 3,728 132.0
Chandler 57.9 176,581 3,050.5
El Mirage 9.7 7,609 786.8
Fountain Hills 18.2 20,235 1,113.8
Gila Bend 22.8 1,980 86.7
Gilbert 43.0 109,697 2,553.7
Glendale 55.7 218,812 3,929.5
Goodyear 116.5 18,911 162.4
Guadalupe 0.8 5,228 6,813.9
Litchfield Park 3.1 3,810 1,216.6
Mesa 125.0 396,375 3,171.3
Paradise Valley 15.5 13,664 881.7
Peoria 138.0 108,364 2,781.9
Phoenix 474.9 1,321,045 167.3
Queen Creek 25.8 4,316 1,100.4
Scottsdale 184.2 202,705 443.9
Surprise 69.5 30,848 3,959.4
Tempe 40.1 158,625 894.1
Tolleson 5.6 4,974 441.7
Wickenburg 11.5 5,082 2,296.1
Youngtown 1.3 3,010 726.8
Gila County Globe 18.0 7,486 415.5
Hayden 1.3 892 707.1
Miami 1.0 1,936 2,008.0
Payson 19.5 13,620 699.6
Winkelman 0.7 443 612.3
Pinal County Apache Junction 34.2 31,814 929.3
Casa Grande 48.2 25,224 523.7
Coolidge 5.0 7,786 1,549.1
Eloy 71.7 10,375 144.8
Florence 8.3 17,054 2,056.2
Kearny 2.8 2,249 805.4
Mammoth 1.1 1,762 1,626.5
Superior 1.9 3,254 1,684.6
33
Jurisdiction Land Area Population Population
Density
Cochise County Benson 35.7 4,711 131.9
Bisbee 4.8 6,090 1,266.3
Douglas 7.7 14,312 1,852.7
Huachuca City 2.8 1,751 626.5
Sierra Vista 153.5 37,775 246.1
Tombstone 5.6 1,504 894.1
Willcox 6.0 3,733 622.3
Graham County Pima 2.5 1,989 787.0
Safford 7.9 9,232 1,166.1
Thatcher 4.4 4,022 919.4
Greenlee County Clifton 14.9 2,596 174.8
Duncan 2.6 812 317.6
Santa Cruz County Nogales 20.8 20,878 1,002.1
Patagonia 1.2 881 738.7
34
35
References
Abdel- Aty, M. A. and A. E. Radwan. 2000. Modeling traffic accident occurrence and
involvement. Accident Analysis and Prevention 32: 633 – 642.
Arizona Department of Transportation. Arizona Motor Vehicle Crash Facts 2000.
Prepared by the Motor Vehicle Division in cooperation with the Traffic Records Section.
Phoenix, 2001.
Chin, H. C. and M. A. Quddus. 2003. Applying the random effect negative binomial
model to examine traffic accident occurrence at signalized intersections. Accident
Analysis and Prevention 35: 253– 259.
Greene, W. 2000. Econometric Analysis. Upper Saddle River, NJ: Prentice Hall.
Harwood, D. W., F. M. Council, E. Hauer, W. E. Hughes, and A. Vogt. 2000. Prediction of
the Expected Safety Performance of Rural Two- Lane Highways. FHWA- RD- 99- 207.
Washington D. C.: Federal Highway Administration.
Hauer, E., J. C. N. Ng, and J. Lovell. 1988. Estimation of safety at signalized
intersections ( with discussions and closure). Transportation Research Record 1185: 48- 61.
Joshua, S. and N. Garber. 1990. Estimating truck accident rate and involvement using
linear and Poisson regression models. Transportation Planning and Technology 15: 41- 58.
Jovanis, P. and H. Chang. 1986. Modeling the relationship of accidents to miles traveled.
Transportation Research Record 1068: 42- 51.
Kim, D.- G., J. Oh, and S. Washington. 2006a. Modeling crash types: new insights into the
effects of covariates on crashes at rural intersections. ASCE Journal of Transportation
Engineering 132 ( 4): 282- 292.
Kim, D.- G., Y. Lee, S. Washington, and K. Choi. 2006b. Modeling crash outcome
probabilities at rural intersections: application of hierarchical binomial logistic models.
Analysis and Prevention 39 ( 1): 125- 134.
Ladron de Guevara, F. and S. Washington. 2004. Forecasting crashes at the planning
level: a simultaneous negative binomial crash model applied in Tucson, Arizona.
Transportation Research Record 1897: 191- 199.
Lord, D., S. Washington, and J. Ivan. 2004. Poisson, Poisson- Gamma, and zero- inflated
regression models of motor vehicle crashes: balancing statistical fit and theory. Accident
Analysis and Prevention 37 ( 1): 35- 46.
36
Lyon, C., J. Oh, B. Persaud, S. Washington, and J. Bared. 2003. Empirical investigation
of interactive highway safety design model accident prediction algorithm: rural
intersections. Transportation Research Record 1840: 78– 86.
Miaou, S., P. Hu, T. Wright, A. Rathi, and S. Davis. 1992. Relationship between truck
accidents and highway geometric design: a Poisson regression approach. Transportation
Research Record 1376: 10– 18.
Mitra, S., H. C. Chin, and M. A. Quddus. 2002. Study of intersection accidents by
maneuver type. Transportation Research Record 1784: 43– 50.
Oh, J., C. Lyon, S. Washington, B. Persaud, and J. Bared. 2003. Validation of the FHWA
crash models for rural intersections: lessons learned. Transportation Research Record
1840: 41– 49.
Oh, J., S. Washington, and K. Choi. 2004. Development of accident prediction models for
rural highway intersections. Transportation Research Record 1897: 18- 27.
Persaud, B. and T. Nguyen. 1998. Disaggregate safety performance models for signalized
intersection on Ontario Provincial roads. Transportation Research Record 1635: 113– 120.
Shankar, V., F. Mannering, and W. Barfield. 1995. Effect of roadway geometric and
environmental factors on rural freeway accident frequencies. Accident Analysis and
Prevention 27 ( 3): 371– 389.
Stutts, J., W. Hunter, and W. Pein. 1996. Pedestrian- vehicle crash types: an update.
Transportation Research Record 1538: 68– 74.
U. S. Bureau of the Census. Census Data for State of Arizona, 2000. Washington D. C.,
2003.
Van Schalkwyk, I., M. Sudeshna, and S. Washington. 2006. Incorporating weather into
region- wide safety planning prediction models. Proceedings of the 85th Transportation
Research Board Annual Meeting.
Vogt, A. and J. Bared. 1998. Accident Prediction Models for Two- Lane Rural Roads:
Segments and Intersections. FHWA- RD- 98- 133. Washington D. C.: Federal Highway
Administration.
Vogt, A. 1999. Crash Models for Rural Intersections: Four- Lane by Two- Lane Stop-
Controlled and Two- Lane by Two- Lane Signalized. FHWA- RD- 99- 128. Washington D. C.:
Federal Highway Administration.
Washington, S., J. Metarko, I. Fomunung, R. Ross, F. Julian, and E. Moran. 1999. An
inter- regional comparison: fatal crashes in the southeastern and non- southeastern United
States: preliminary findings. Accident Analysis & Prevention 31 ( 102): 135- 146.
37
Washington, S., M. Karlaftis, and F. Mannering. 2003. Statistical and Econometric
Methods for Transportation Data Analysis. Boca Raton, FL: Chapman and Hall.
Washington, S., M. Meyer, I. van Schalkwyk, E. Dunbaugh, S. Mitra, and M. Zoll. 2006.
Incorporating Safety into Long Range Transportation Planning. NCHRP 8- 44.
Washington D. C.: Transportation Research Board.
White, D. and S. Washington. 2001. Safety restraint use rate as a function of law
enforcement and other factors: preliminary analysis. Transportation Research Record
1779: 109- 115.
Zellner, A. 1962. An efficient method of estimating seemingly unrelated regressions and
tests for aggregation bias. Journal of the American Statistical Association 57 ( 298): 348–
368.

Click tabs to swap between content that is broken into logical sections.

Copyright to this resource is held by the creating agency and is provided here for educational purposes only. It may not be downloaded, reproduced or distributed in any format wihtout written permission of the creating agency. Any attempt to circumvent the access controls placed on this file is a violation of United States and international copyright laws, and is subject to criminal prosecution.

Feasibility of Forecasting Highway
Safety in Support of Safety
Incentive and Safety Target
Programs
Final Report 597
Prepared by:
Simon Washington, Ph. D.
and
Do- Gyeong Kim
Department of Civil and Environmental Engineering
Arizona State University
Tempe, Arizona
November 2007
Prepared for:
Arizona Department of Transportation
206 South 17th Avenue
Phoenix, Arizona 85007
and
Arizona Governor’s Office of Highway Safety
In cooperation with
U. S. Department of Transportation
Federal Highway Administration
National Highway Traffic Safety Administration
The contents of this report reflect the views of the authors who are responsible for the
facts and the accuracy of the data presented herein. The contents do not necessarily
reflect the official views or policies of the Arizona Department of Transportation or the
Federal Highway Administration. This report does not constitute a standard, specification,
or regulation. Trade or manufacturers' names which may appear herein are cited only
because they are considered essential to the objectives of the report. The U. S.
Government and the State of Arizona do not endorse products or manufacturers.
Technical Report Documentation Page
1. Report No.:
FHWA- AZ- 06- 597
2. Government Accession No. 3. Recipient’s Catalog No.
4. Title and Subtitle
Feasibility of Forecasting Highway In Support of Safety Incentive
and Safety Target Programs
5. Report Date:
November 2007
6. Performing Organization Code
7. Authors: Drs. Simon Washington and Do- Gyeong Kim 8. Performing Organization Report No.
9. Performing Organization Name and Address
Arizona State University
Department of Civil & Environmental Engineering
Tempe, AZ 85287- 5306
10. Work Unit No.
11. Contract or Grant No.
SPR- PL- 1-( 61) 597
12. Sponsoring Agency Name and Address
Arizona Department of Transportation
206 S. 17th Avenue
Phoenix, AZ 85007
13. Type of Report & Period Covered
Final Report
14. Sponsoring Agency Code
15. Supplementary Notes:
Prepared in cooperation with the Arizona Governor’s Office of Highway Safety and the U. S.
Department of Transportation, Federal Highway Administration & National Highway Traffic
Safety Administration
16. Abstract
Using the frequency of fatal crashes from the current observation period ( e. g. month, year, etc.) as the
prediction of expected future performance does not account for changes in safety that result from
increases in exposure ( population, additional roads, new drivers, etc.). This effect is especially
pronounced in rapidly growing regions, where safety changes are anticipated in the absence of safety
investment programs. The objective of this study was to examine the feasibility of predicting future
fatal motor vehicle crashes given changes in future risk exposure, so that reasonable safety ‘ targets’
can be established in support of a safety incentive or safety target programs. Safety incentive or
target programs can be used to set future safety targets ( i. e. fatal crashes) for jurisdictions in Arizona.
17. Key Words
Safety forecasting, fatal crashes, safety
planning, safety management
18. Distribution Statement
Document is available to the
U. S. public through the
National Technical Information
Service, Springfield, Virginia
22161
23. Registrant’s Seal
19. Security Classification
Unclassified
20. Security Classification
Unclassified
21. No. of Pages
41
22. Price
SI* ( MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By To Find Symbol
LENGTH LENGTH
in inches 25.4 millimeters mm mm millimeters 0.039 inches in
ft feet 0.305 meters m m meters 3.28 feet ft
yd yards 0.914 meters m m meters 1.09 yards yd
mi miles 1.61 kilometers km km kilometers 0.621 miles mi
AREA AREA
in2 square inches 645.2 square millimeters mm2 mm2 Square millimeters 0.0016 square inches in2
ft2 square feet 0.093 square meters m2 m2 Square meters 10.764 square feet ft2
yd2 square yards 0.836 square meters m2 m2 Square meters 1.195 square yards yd2
ac acres 0.405 hectares ha ha hectares 2.47 acres ac
mi2 square miles 2.59 square kilometers km2 km2 Square kilometers 0.386 square miles mi2
VOLUME VOLUME
fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ounces fl oz
gal gallons 3.785 liters L L liters 0.264 gallons gal
ft3 cubic feet 0.028 cubic meters m3 m3 Cubic meters 35.315 cubic feet ft3
yd3 cubic yards 0.765 cubic meters m3 m3 Cubic meters 1.308 cubic yards yd3
NOTE: Volumes greater than 1000L shall be shown in m3.
MASS MASS
oz ounces 28.35 grams g g grams 0.035 ounces oz
lb pounds 0.454 kilograms kg kg kilograms 2.205 pounds lb
T short tons ( 2000lb) 0.907 megagrams
( or “ metric ton”)
mg
( or “ t”)
mg megagrams
( or “ metric ton”)
1.102 short tons ( 2000lb) T
TEMPERATURE ( exact) TEMPERATURE ( exact)
º F Fahrenheit
temperature
5( F- 32)/ 9
or ( F- 32)/ 1.8
Celsius temperature º C º C Celsius temperature 1.8C + 32 Fahrenheit
temperature
º F
ILLUMINATION ILLUMINATION
fc foot candles 10.76 lux lx lx lux 0.0929 foot- candles fc
fl foot- Lamberts 3.426 candela/ m2 cd/ m2 cd/ m2 candela/ m2 0.2919 foot- Lamberts fl
FORCE AND PRESSURE OR STRESS FORCE AND PRESSURE OR STRESS
lbf poundforce 4.45 newtons N N newtons 0.225 poundforce lbf
lbf/ in2 poundforce per
square inch
6.89 kilopascals kPa kPa kilopascals 0.145 poundforce per
square inch
lbf/ in2
SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380
Table of Contents
Motivation for Study............................................................................................................ 1
Background and Relevant Research .................................................................................... 3
Data Collection and Description.......................................................................................... 5
Methodological Approach and Modeling Results ............................................................. 17
Procedure to Apply the Safety Incentive or Safety Target Forecasting Model ................. 21
Conclusions and Recommendations .................................................................................. 23
Appendix A: Questionnaire Sent to Jurisdictions.............................................................. 27
Appendix B: Arizona Population and Population Change Statistics
by Jurisdiction ( 2000) ................................................................................ 28
Appendix C: Arizona Population Density by Jurisdiction ( 2000) ..................................... 31
References..................................................................................................................... .... 35
List of Tables
Table 1: Description and Measurement of Variables Used in the Analysis ........................ 6
Table 2: The Percent Change in Arizona Population from 1990 to 2000 by County.......... 7
Table 3: Arizona Land Areas by County in 2000 ................................................................ 9
Table 4: Arizona Population Densities by County in 2000 ............................................... 10
Table 5: Arizona Population of Elderly, Young, and Minorities by County in 2000........ 11
Table 6: Arizona Number of Housing Units, Density, and Persons per Household
by County in 2000............................................................................................... 12
Table 7: Arizona Number of Employees and Mean Travel Time to Work
by County in 2000............................................................................................... 13
Table 8: Arizona Total and Fatal Crashes by Jurisdiction in 2000.................................... 14
Table 9: Negative Binomial Model Estimation Results of Fatal Crashes
with Complete Set of Predictors ......................................................................... 19
Table 10: Three New Fatal Crash Models and Comparison
to Previously Estimated Models ...................................................................... 20
Table 11: Example 1: Excel Prediction Spreadsheet for Fatal Crash Prediction Model ... 21
Table 12: Example 2: Excel Prediction Spreadsheet for Fatal Crash Prediction Model ... 22
Table 13: Description of Important Predictor Variables for Safety Forecasting Model.... 24
List of Figures
Figure 1: Location of Counties and COGs/ MPOs in Arizona ............................................. 5
Figure 2: Percentage of Total Arizona Population by County in 2000................................ 8
Figure 3: Correlation Matrix of Predictor Variables.......................................................... 18
List of Acronyms
ADOT Arizona Department of Transportation
AADT Annual Average Daily Traffic
DOT Department of Transportation
GHSA Governors’ Highway Safety Association
MPO Metropolitan Planning Organization
PPHH Persons Per Household
TAZ Traffic Analysis Zone
VMT Vehicle Miles Traveled
1
Motivation for Study
Approximately 43,000 people die on the nation’s roads each year. In addition, motor
vehicle crashes are the leading cause of death or injury for persons from age 2 through 33.
These traffic fatality and injury statistics have led to significant interest in highway safety
investments that will save lives.
One relatively unexplored area of research is the setting of safety targets, incentives, or
milestones for jurisdictions. For example, a region may want to achieve a measurable
decrease in pedestrian- involved fatal crashes in a future time period. Using simply the
baseline ( e. g., the current year’s) crash frequencies ( e. g., fatal crashes, injury crashes,
etc.) to set performance targets is inadequate, especially in rapidly developing states such
as Arizona, since the impacts of growth alone will affect the expected safety of a region
or jurisdiction. Specifically, increased vehicle miles traveled ( VMT), increased
population, new drivers, and new facilities will lead to an increase in expected crashes.
Under these circumstances, the current frequency of crashes is not a reliable estimate of
future expected crashes.
Crash prediction models based on statistical or econometric modeling techniques have
been developed for a variety of purposes; most commonly to estimate the expected crash
frequencies from various roadway entities ( highways, intersections, interstates, etc.) and
also to identify geometric, environmental, and operations factors that are associated with
crashes. The vast majority of these models have been developed to forecast crashes on
roadway links and intersections— a scale that is too fine and too cumbersome for
forecasting crashes at the jurisdiction or regional scale.
Agencies, such as departments of transportation ( DOTs) and the Governors’ Highway
Safety Association ( GHSA), may benefit from tools that enable the setting of future
safety targets. These targets may be used to support incentive- based programs within a
jurisdiction— offering incentives based on how many motor- vehicle– related fatalities
( and/ or injuries) are reduced by a region’s safety investment program.
To support an incentive based program, it is necessary to be able to accurately forecast
what safety targets are expected to be in a region or jurisdiction in a future time period,
given changes in road mileage, population, land area, VMT, and so on. This can be
accomplished by estimating crash prediction models using aggregate jurisdiction- level
characteristics as predictors. Of course a defensible and comprehensive set of predictors
must be collected in order to produce a reliable and precise forecasting model.
The purpose of this research is to examine the feasibility of developing a safety
forecasting model in Arizona to support both or either a safety incentive or a safety target
program. A safety incentive program in concept would offer incentives ( e. g., project
funds) for jurisdictions able to show reductions in crashes ( e. g., fatal) due to
implementation of effective safety programs. It is not known whether safety incentive
programs would be adopted or are attractive to jurisdictions or to Metropolitan Planning
Organizations ( MPOs)— but the concept has been raised and discussed in professional
2
forums. It is known, however, that in order to set reasonable safety goals— such as goals
established in a statewide safety management plan— one must be able to forecast the
expected total crashes and fatal crashes within jurisdictions given the planned growth in
population, road mileage, etc. expected over various growth time horizons. Thus, the
need to forecast safety targets has largely been overlooked in Arizona and the U. S. as a
whole.
Motor vehicle crash data along with exposure- related safety data obtained from the U. S.
Census, ADOT, and through questionnaires sent to Arizona jurisdictions were used to
develop the forecasting models and methodology for this project. The models are
intended to enable transportation safety practitioners and decision makers to better
understand the relationship between fatalities and exposure- related safety variables,
especially in jurisdictions with rapid growth, so that future safety targets can be set.
The remainder of this report provides additional background and review of previous
research regarding jurisdiction- level crash forecasting models. The data collected in
support of this research effort are then described. A description of the modeling approach
used in this research is followed by a discussion of modeling results. The procedure to
apply the safety incentive or safety target forecasting model is then given, with two
example applications. Finally, conclusions and recommendations are provided.
3
Background and Relevant Research
The safety profession is replete with models that predict crashes at the microscopic
level— say for intersections or for road segments ( see Bibliography for extensive
examples). These models, however, do not address the forecasting of crashes at more
aggregate levels. Very little research has addressed this issue, and much work is ongoing
in this area of research ( Washington et al. 2006). Other research efforts on aggregate level
forecasting are currently underway at Ryerson Polytechnic University, Purdue University,
and the University of British Columbia. Despite the little research that has been
conducted in this area, much has been learned from prior research on microscopic crash
models.
A reasonable question to ask is: “ Are macroscopic, or jurisdiction- level, statistical models
defensible and logically feasible?” The following arguments, based on accepted
principles and logic from the road safety and statistics communities, support the use of
aggregate level safety prediction models.
1. Crashes are largely random events. Much research has shown that human errors
account for 60% to 90% of crashes. Thus, many crashes are more a function of
human- related factors rather than roadway- related factors. As simple examples,
crashes that result from a driver tuning a radio, answering a cell phone, following
another vehicle too closely, speeding, or running a red light are events that occur
somewhat randomly on a network. It is easy to understand, then, that modeling
crashes at the segment or intersection level is challenging, because there is a large
random component to crashes that is not explained by local road characteristics.
At a more aggregate level, in contrast, crashes are related to aggregate predictors,
such as population demographics, ‘ high risk’ driving populations, the general
classes of road facilities, etc., and assigning crashes to specific links or segments
is not necessary. Thus, by aggregating the transportation system at the Traffic
Analysis Zone( TAZ) 1 level or higher , some of the difficulties caused by
‘ lumpiness’ of random events that we see across intersections or across road
segments are reduced.
2. Aggregate safety differences are substantiated by research. Much research
supports that safety is related to aggregate measures of exposure. First order
effects are revealed as more VMT and crashes, and population and crashes are
strongly and positively correlated. Older drivers suffer from reduced reaction and
perception times, as well as reduced vision and flexibility. Younger drivers suffer
from inexperience and aggressiveness. Minorities have been shown to wear safety
restraints less than whites, and restraint use in rural areas is less than in urban
areas. Interstates have relatively low crash rates, while rural roads with high
speeds have more serious- injury crashes. Crashes in urban areas are attended by
emergency medical services more quickly than crashes in rural areas.
Intersections are locations of complex traffic movements and thus have greater
1 TAZ is the unit of analysis used in metropolitan planning level travel demand models.
4
numbers of crashes than road segments. Increasing traffic congestion tends to
reduce crash severity. School zones are associated with bicycle and pedestrian
crashes. These well supported aggregate relationships, and others not listed here,
are the relationships captured in aggregate level prediction models. The aggregate
relationships described above form the basis for the statistical modeling at the
TAZ level. It is the reliance on these ‘ average’ relationships, and characteristics
measured at the TAZ level, on which model predictions are based.
3. Models for predicting have fewer restrictions than models for explaining.
Intersection and road- segment level accident prediction models are usually held to
a high standard, as they are often used both to predict the expected performance
of such facilities but also to explain relationships between variables. Often, and
sometimes wrongly, these microscopic models are used to infer the effects of
countermeasures, such as the safety effect of the presence of a left- turn lane on
angle crashes. When a model is used simply for prediction, however, and not
inference, there is greater flexibility in model estimation and variable selection
choices. The PLANSAFE model is intended only for prediction, not explanation.
( See Washington et al. 2006 for a discussion of the PLANSAFE model used for
forecasting safety.) Thus, for example, if a population variable is used to predict
fatal crashes per TAZ, its estimated coefficient is used solely in the prediction
equation but is not interpreted to have specific explanatory marginal effects.
These three arguments, or justifications, form the basis for the development of
jurisdiction- level accident prediction models. A consequence of these arguments,
however, is that the models cannot be used for explanation of crash causation or for the
assessment of roadway- specific countermeasures. The aggregate relationships modeled
are suitable for predicting a hypothetical or future outcome should the set of predictors be
changed. This restriction is not too dissimilar from the restriction placed on travel
demand models, whose primary purpose is to predict demand for roadway space of motor
vehicles in hypothetical or future scenarios.
We must also recognize that aggregation reduces the variability and can lead to ecological
correlation, which can lead to interpretation problems. Thus, we must proceed carefully
to examine the forecasting models, to interpret them with caution, and to apply them as
they are intended— to predict future trends in safety given aggregate changes in exposure.
5
Data Collection and Description
Estimating jurisdiction- level crash prediction models to predict safety requires aggregate
information such as socio- economic, demographic, and transportation related data. In
particular, data related to established risk exposure variables are needed.
The analysis unit of this research is the jurisdiction ( cities and towns), since the objective
of this research is to examine how jurisdictional characteristics influence safety. Arizona
consisted of 87 jurisdictions within 15 counties ( as of 2005), which are divided into the
six regional Councils of Governments ( COG) for multi- jurisdictional regional planning as
shown in Figure 1: Central Arizona Association of Governments ( CAAG), Maricopa
Association of Governments ( MAG), Northern Arizona Council of Governments
( NACOG), Pima Association of Governments ( PAG), South Eastern Arizona
Governments Organization ( SEAGO), and Western Arizona Council of Governments
( WACOG). Of course these COG boundaries change over time and currently new COGs
have been formed within the state.
Figure 1: Location of Counties and COGs/ MPOs in Arizona
As mentioned previously, the required input data for the analysis are aggregated by
jurisdiction. The aggregate data came from three sources: crash data, census data, and
through mail surveys. Crash data were collected from the 2000 Arizona Crash Facts
which was published by the Arizona Department of Transportation ( ADOT 2001).
Jurisdiction- level characteristics used for predictors were obtained from Census 2000
data, which includes a variety of socio- demographic information related to people,
business, and geography that is maintained by the U. S. Census Bureau. Since some of the
census data were available only for the year 2000, the number of fatalities that occurred
6
in 2000 was used in the analysis. In addition, the survey response rate was quite
unsatisfactory ( 17 out of 87 surveys were returned, or about 20% response rate, some of
which were incomplete), and so additional variables thought to be important for safety
forecasting were dropped from the analysis. Thus, the analysis is based on results from
2000 crash and census data. The questionnaire sent to jurisdictions is shown in Appendix A.
Jurisdiction- Level Safety Predictors
Although numerous jurisdiction- level safety predictors can be obtained from the U. S.
Census Bureau 2000 data, this research employed nine characteristics for the analysis as
predictors: population change, population density, the percentage of elderly people, the
percentage of young people, the proportion of minorities, the number of dwelling units
per acre, persons per household, number of employees, and mean travel time to work.
Table 1 shows the abbreviated names of the variables and their units of measurement. In
the following section, the characteristics of these nine variables are described in relation
to safety.
VARIABLE DESCRIPTION
PERCHAN The percent change in population from 1990 to 2000
POPDEN Population density ( population/ square mile)
POPELDER Persons aged 65 years old or more as a percentage of the total
population
POPYOUNG Persons aged 17 years old or less as a percentage of the total
population
POPMINOR Total number of minorities as a portion of the total population
HUDEN Number of housing units per square mile
PPHH Persons per household
EMPLOY The number of employees as a percentage of the total population
MTT Mean travel time to work ( minutes), workers age 16+
Table 1: Description and Measurement of Variables Used in the Analysis
Population Change
Crashes are likely to be affected by growth because a jurisdiction is coping with its
growth of infrastructure and population above and beyond what is captured by population
alone. For example, a rapidly growing city is more likely to have new construction
projects, new housing projects, new drivers, business growth, and improvements to the
transportation infrastructure ( upgrading of segments and intersections). These attributes
7
are more likely to be associated with additional crashes compared to a city with no
population growth. The percent change in population was used to capture this effect.
The population of Arizona in 1990 was 3,665,339, while the population in 2000 was
5,130,632, an increase of 40.0% over ten years. Maricopa County had the largest
population in Arizona, but with respect to the percent population change, Mohave County
had the highest as shown in Table 2. In contrast, Greenlee County had the smallest
change in population— a modest 6.7% increase.
County Population
In 1990
Population
In 2000 Change (%)
Mohave County 93,497 155,032 65.8
La Paz County 13,844 19,715 42.4
Yuma County 106,895 160,026 49.7
Pima County 666,957 843,746 26.5
Apache County 61,591 69,423 12.7
Coconino County 96,591 116,320 20.4
Navajo County 77,674 97,470 25.5
Yavapai County 107,714 167,517 55.5
Maricopa County 2,122,101 3,072,149 44.8
Gila County 40,216 51,335 27.6
Pinal County 116,397 179,727 54.4
Cochise County 97,624 117,755 20.6
Graham County 26,554 33,489 26.1
Greenlee County 8,008 8,547 6.7
Santa Cruz County 29,676 38,381 29.3
TOTAL 3,665,339 5,130,632 40.0
Table 2: The Percent Change in Arizona Population from 1990 to 2000 by County
8
As shown in Figure 2, more than 75% of the people in Arizona in 2000 lived in Pima and
Maricopa counties ( 16.45% and 59.88%, respectively). In contrast, 0.17% and 0.38% of
population lived in Greenlee and La Paz counties, respectively. With respect to the
population by jurisdiction, approximately 35% of Arizona residents lived in the cities of
Phoenix and Tucson. Phoenix has the highest population, while Jerome has the smallest
population. The population and percent change by jurisdiction is shown in Appendix B.
Figure 2: Percentage of Total Arizona Population by County in 2000
Population Density
It is reasonable to believe that crashes are more likely to occur in urban areas rather than
rural areas because urban areas have higher accident exposures with regard to Annual
Average Daily Traffic ( AADT) and VMT than rural areas. However, when fatal crashes
are examined the opposite relationship is expected. Rural areas are associated with higher
speeds and generally non- median roadways ( i. e., highways vs. freeways), and thus
crashes tend to be more severe on these facilities. Also, congestion in urban areas tends to
limit speeds, which in turn reduces crash severities. Thus, degree of urbanization should
be negatively associated with fatal crashes and positively associated with total crashes.
The population density of a jurisdiction is calculated by dividing the population by land
area of the jurisdiction.
9
Arizona covers 114,006 square miles ( 113,642 square miles of land areas and 364 square
miles of water areas), making it the sixth largest of the 50 states. Despite the vast area,
Arizona has a relatively small number of counties ( 15). Coconino is the largest county
( 18,617.4 square miles); Santa Cruz is the smallest ( 1,237.6 square miles). Table 3 ( p. 8)
shows the counties’ land areas. .
Councils of Governments County Land Area
Mohave County 13,311.6
WACOG La Paz County 4,500.0
Yuma County 5,514.1
PAG Pima County 9,186.3
Apache County 11,204.9
Coconino County 18,617.4
Navajo County 9,953.2
NACOG
Yavapai County 8,123.3
MAG Maricopa County 9,203.1
Gila County 4,767.7
CAAG
Pinal County 5,369.6
Cochise County 6,169.4
Graham County 4,629.3
Greenlee County 1,847.0
SEAGO
Santa Cruz County 1,237.6
TOTAL 113,634.6
Table 3: Arizona Land Areas by County in 2000
10
The average population density of Arizona in 2000 was 45.2 persons per square mile.
Maricopa County had the highest of the 15 counties ( 333.8/ mi2), whereas La Paz County
had the lowest ( 4.4/ mi2) Table 4 shows the population density of all the counties. In terms
of population density by city, Guadalupe had the highest density ( 6,813.9), while
Buckeye had the lowest density ( 44.8). Population densities by jurisdiction— the unit of
analysis used for modeling— are summarized in Appendix C.
County Land Area Population Population
Density
Mohave County 13,311.6 155,032 11.6
La Paz County 4,500.0 19,715 4.4
Yuma County 5,514.1 160,026 29.0
Pima County 9,186.3 843,746 91.8
Apache County 11,204.9 69,423 6.2
Coconino County 18,617.4 116,320 6.2
Navajo County 9,953.2 97,470 9.8
Yavapai County 8,123.3 167,517 20.6
Maricopa County 9,203.1 3,072,149 333.8
Gila County 4,767.7 51,335 10.8
Pinal County 5,369.6 179,727 33.5
Cochise County 6,169.4 117,755 19.1
Graham County 4,629.3 33,489 7.2
Greenlee County 1,847.0 8,547 4.6
Santa Cruz County 1,237.6 38,381 31.0
TOTAL 113,634.6 5,130,632 45.2
Table 4: Arizona Population Densities by County in 2000
11
The Percentage of Elderly and Young Populations
The percentages of elderly and young people are factors that are related to crashes, as
mentioned previously. Young drivers are generally inexperienced, while elderly drivers
suffer from reduced perception and reaction times as well as crash survivability. A total of
667,839 people, about 13.0% of the population, were 65 years old or more in Arizona in
2000. A total of 1,150,466 people, about 22.4% of the population, were 17 years old or
less in 2000. Of the 15 counties, Maricopa County had the highest number of both elderly
and young people, and with respect to jurisdictions, Phoenix had the highest number of
both elderly and young people.
Besides these age- related factors, this research employs the proportion of minorities as a
predictor of severe crashes. Minorities, on average, wear safety restraints less than whites
( see White et al. 2001 and Washington et al. 1999) and tend to drive older vehicles with
less extensive safety features ( compared to new vehicles). Phoenix was found to have the
highest number of minorities. Table 5 shows the number of elderly, young, and minorities
by county.
County Elderly People Young People Minority
Mohave County 20,801 19,063 15,786
La Paz County 2,139 977 1,967
Yuma County 12,388 26,681 62,785
Pima County 66,911 111,925 236,186
Apache County 1,002 2,555 2,488
Coconino County 3,689 13,239 19,779
Navajo County 3,798 8,791 11,318
Yavapai County 22,056 16,699 14,401
Maricopa County 276,354 672,338 1,000,267
Gila County 5,664 4,657 6,289
Pinal County 16,017 19,974 42,397
Cochise County 10,191 15,538 31,654
Graham County 2,327 3,740 5,410
Greenlee County 371 922 1,824
Santa Cruz County 2,448 6,159 20,105
TOTAL 667,839 1,150,466 1,856,374
Table 5: Arizona Population of Elderly, Young, and Minorities by County in 2000
12
Residential Dwelling Density and Persons per Household
Residential dwelling density ( the number of housing units per square mile) and persons
per household were also used as predictors to model jurisdiction- level crash prediction
models ( see Table 6). Residential dwelling density is a surrogate for the compactness of
development— which corresponds to high intersection intensity ( the questionnaire in
Appendix A tried to capture this more explicitly). Persons per household might reflect
socio- economic status, which may correlate with vehicle age and safety equipment,
employment, etc. The total number of housing units over 87 jurisdictions within 15
counties was 1,660,557. Of the 15 counties, Maricopa County and La Paz County had the
highest and smallest house densities, respectively. With respect to residential density by
jurisdiction, South Tucson was the highest ( 2,059.0) whereas Buckeye was the lowest
( 16.1).
The number of persons per household ( PPHH) for the 87 Arizona jurisdictions ranged
from 1.74 ( Youngtown) to 7.51 ( Colorado City), while the average number of persons per
household was 2.79. Unlike residential density, Colorado City was found to have the
highest and Youngtown the lowest persons per household respectively.
County Number of
Housing Units
Housing Density Average Number
of PPHH
Mohave County 50,509 1,273.4 2.45
La Paz County 4,343 140.4 2.32
Yuma County 40,911 2,419.7 2.86
Pima County 232,563 3,734.6 2.47
Apache County 4,001 440.4 3.41
Coconino County 25,661 582.6 2.80
Navajo County 14,768 874.8 3.17
Yavapai County 45,725 2,267.8 2.33
Maricopa County 1,139,705 14,507.4 2.67
Gila County 11,663 2,001.0 2.50
Pinal County 46,014 3,682.0 2.68
Cochise County 30,344 2,272.2 2.55
Graham County 5,880 1,089.0 2.99
Greenlee County 1,471 220.6 2.73
Santa Cruz County 6,999 727.5 3.23
TOTAL 1,660,557 36,233.4 2.79
Table 6: Arizona Number of Housing Units, Density, and Persons per Household
by County in 2000
13
Number of Employees and Mean Travel Time to Work
Relatively large numbers of employees lead to an increase in the number of trips, which
increases traffic volume, and the increased trips and traffic volume may also increase
exposure to the risk of motor- vehicle- related crashes. Also, work trips tend to include
aggressive and/ or distracted drivers. Consequently, the higher number of employees
might be highly correlated with the higher crash frequencies. Due to the potential
correlation between the number of employees and crash frequencies, the number of
employees was included as an independent variable.
Similarly, crash frequencies might be expected to increase as mean travel time to work
grows because the longer travel times suggest higher exposure levels and greater levels of
driver fatigue. The mean travel time to work in Arizona is 22.1 minutes, as shown in Table 7.
County Number of Employees Mean Travel Time to Work
( minutes)
Mohave County 78,758 20.6
La Paz County 5,453 17.2
Yuma County 73,596 18.6
Pima County 420,263 23.9
Apache County 6,600 28.0
Coconino County 49,627 19.0
Navajo County 23,894 22.9
Yavapai County 80,491 22.5
Maricopa County 2,148,360 26.1
Gila County 19,535 20.3
Pinal County 77,672 27.4
Cochise County 53,114 19.8
Graham County 11,276 22.6
Greenlee County 2,421 20.3
Santa Cruz County 14,982 19.7
TOTAL 3,006,042 22.1
Table 7: Arizona Number of Employees and Mean Travel Time to Work
by County in 2000
Jurisdiction- Level Crash Data
As mentioned previously, crash data used in this research were obtained from the 2000
Arizona Crash Facts. In that year, 131,368 crashes and 891 fatal crashes occurred in Ari-zona.
Excluding crashes that occurred within a specific county but not within a specific
city ( e. g., state rural roads in Apache County experienced 358 total crashes and 10 fatal
crashes in 2000), 108,176 total crashes and 392 fatal crashes occurred in the 87 Arizona
jurisdictions ( cities or towns). Of the 87 jurisdictions, the City of Phoenix had the greatest
14
number of total crashes and fatal crashes, with 44,146 crashes and 168 fatal crashes
reported. Zero crashes were reported in eight jurisdictions, whereas a total of 47 juris-dictions
reported zero fatal crashes in 2000. Table 8 presents the frequency of total crashes
and fatalities across the 87 Arizona jurisdictions in 2000 ( excluding crashes occurring on
state rural roads or other rural roads outside a jurisdiction but within the county).
As shown in table 8, crash frequencies by jurisdiction for fatal crashes are quite small
relative to total crashes. As a result, statistical models based on total crashes will tend to
be more reliable than those on fatal crash data. Also of note is the preponderance of
zeroes reported in the fatal crash column. A large number of zeroes is a common
phenomenon with fatal crash data across analysis units. These zeroes tend to raise
challenges in the estimation of statistical models, as described by Lord et al. ( 2004). In
the analysis that follows we generally follow the advice of Lord et al. ( 2004) in dealing
with the ‘ excess’ zeroes.
County Jurisdiction Total Crashes Fatal Crashes
Cochise County Benson 36 0
Bisbee 48 1
Douglas 321 1
Huachuca City 7 1
Sierra Vista 775 2
Tombstone 19 0
Willcox 39 0
Graham County Pima 14 0
Safford 113 0
Thatcher 48 0
Greenlee County Clifton 30 0
Duncan 0 0
Santa Cruz County Nogales 411 1
Patagonia 0 0
TOTAL 1,861 6
Mohave County Bullhead City 673 4
Colorado City 17 0
Kingman 400 1
Lake Havasu City 525 6
La Paz County Parker 16 0
Quartzsite 38 0
Yuma County San Luis 0 0
Somerton 16 0
Wellton 1 0
Yuma 1,489 3
TOTAL 3,175 14
Table 8 Arizona Total and Fatal Crashes by Jurisdiction in 2000
15
County Jurisdiction Total Crashes Fatal Crashes
Pima County Marana 545 1
Oro Valley 263 2
Sahuarita 40 0
South Tucson 181 0
Tucson 14,822 52
TOTAL 15,851 55
Apache County Eagar 44 0
Saint Johns 25 0
Springerville 1 0
Coconino County Flagstaff 2,480 7
Fredonia 3 0
Page 123 2
Williams 53 2
Navajo County Holbrook 83 1
Pinetop- Lakeside 96 0
Show Low 133 0
Snowflake 80 1
Taylor 6 0
Winslow 162 1
Yavapai County Camp Verde 89 0
Chino Valley 83 3
Clarkdale 0 0
Cottonwood 196 1
Jerome 10 0
Prescott 883 2
Prescott Valley 357 2
Sedona 0 0
TOTAL 4,907 22
Maricopa County Avondale 473 0
Buckeye 6 2
Carefree 9 0
Cave Creek 10 0
Chandler 3,056 4
El Mirage 114 3
Fountain Hills 69 0
Gila Bend 18 0
Gilbert 1,352 7
Glendale 4,997 27
Goodyear 249 4
Table 8 continued
16
County Jurisdiction Total Crashes Fatal Crashes
Maricopa County Guadalupe 35 0
( continued) Litchfield Park 0 0
Mesa 11,019 30
Paradise Valley 239 0
Peoria 1,554 1
Phoenix 44,146 168
Queen Creek 0 0
Scottsdale 4,555 19
Surprise 244 3
Tempe 8,453 16
Tolleson 125 0
Wickenburg 97 2
Youngtown 0 0
TOTAL 80,820 286
Gila County Globe 141 0
Hayden 5 1
Miami 24 0
Payson 139 0
Winkelman 2 0
Pinal County Apache Junction 331 3
Casa Grande 661 2
Coolidge 82 0
Eloy 83 2
Florence 60 1
Kearny 4 0
Mammoth 9 0
Superior 21 0
TOTAL 1,562 9
Table 8 continued
17
Methodological Approach and Modeling Results
Methodological Approach
Two different approaches are generally used to estimate crash predictions, Poisson
regression and negative binomial regression ( Jovanis and Chang 1986; Washington et al.
2003), although various other modeling approaches are possible ( see for example Lord et
al. 2004). Crash counts are approximated well by a Poisson process ( Joshua and Garber
1990), since crash counts are discrete, positive integers. The Poisson regression model
requires that the variance of the crash frequency is approximately equal to its mean. In
much of the observed crash data, however, the variance of the crash frequency is greater
than the mean and overdispersion occurs ( Miaou et al. 1992). Miaou et al. introduced the
negative binomial distribution for modeling traffic safety which accommodates greater
variance in the data than allowed by the Poisson distribution. The overdispersion
typically arises from variation in crash means across sites. As a result, the negative
binomial regression model is the preferred modeling approach when overdispersion is
present ( Washington et al. 2003). This research employs the negative binomial regression
model to develop jurisdiction- level crash prediction models. The negative binomial
regression model is briefly summarized in the following section.
The Negative Binomial regression model specifies a relationship between the expected
number of crashes occurring at the ith element and the q parameters, Xi1, Xi2, …, Xiq, as
follows:
( ) exp( ) i i 0 1 i1 2 i2 q iq i E y = μ = β + β X + β X + 􀀢 􀀢 + β X + ε
In addition, the Negative Binomial regression model includes a quadratic term in the
variance to reflect overdispersion in the model variance. As a result, the Negative
Binomial regression model takes the following form:
μ α
μ
α
α
− + +
+ −
=
i
i
y
y
i
i
i y
P y y
!( 1)! ( 1 )
() ( 1)! ,
where α is the overdispersion parameter and the variance is:
( ) ( ) 2 i i i Var y = μ + α μ .
The overdispersion or extra- Poisson variation is generally due to variables omitted from
the model that explain variation in crashes between sites. If α is equal to 0, the Negative
Binomial reduces to a Poisson model. The value of α corresponds with the degree of
overdispersion over and above that associated with the mean i μ
.
Similar to previous studies, the final model structure used is
( ) exp i jij Ey = Σβx
where ( ) i E y is the expected number for jurisdiction i, ij x ’ s are variables describing
safety- related exposure variables for jurisdictions, and the βj are estimated parameters or
effects of the predictor variables.
Modeling Results
First, we examined the correlation between independent variables, since one of the
problems with multiple regression is that explanatory variables may be correlated, thus
confounding the effects of variables with one another. In particular, regression
coefficients that indicate the effect of one factor may change when some other factor is
added or removed from the model.
Figure 3 shows the correlation between independent variables used in the study. Using
statistical tests of significant correlation, it was found that the percentage of young people
( POPYOUNG) and persons per household ( PPHH) are highly positively correlated with
ρ = 0.8545, whereas the percentage of young people ( POPYOUNG) and the number of
employees ( EMPLOY) are highly negatively correlated with ρ =- 0.972.
Correlation Matrix
perchan popden popelder popyoung popminor huden pphh emppop mtt
perchan 1.0000
popden 0.0610 1.0000
popelder 0.0093 - 0.1262 1.0000
popyoung - 0.0863 0.1185 - 0.7084 1.0000
popminor - 0.1699 0.3595 - 0.4187 0.4282 1.0000
huden - 0.0940 0.7464 - 0.0131 - 0.0360 0.2525 1.0000
pphh - 0.0071 0.1794 - 0.5845 0.8545 0.3720 - 0.0172 1.0000
emppop 0.0986 - 0.1061 0.7401 - 0.9720 - 0.4379 0.0433 - 0.8188 1.0000
mtt 0.4228 0.1901 - 0.0255 0.0895 - 0.0534 0.1674 0.1382 - 0.0653 1.0000
Figure 3: Correlation Matrix of Predictor Variables
The explanatory variables described in Table 1 were used in the software program
LIMDEP ( copyright William Greene) to choose the significant variables for the
jurisdiction- level fatal crash model. One of the disadvantages with the LIMDEP software
is that the LIMDEP does not automate the process of removing insignificant variables
from the model, one at a time, until only significant variables are left in the model. Thus,
various models were tested to estimate the possible nature of the relationships between
the independent variables and fatal crashes, beginning with a ‘ full’ model with many
variables. Table 9 presents the estimation results for a fatal crash model with a ‘ full’
( complete) set of predictor variables.
18
19
Among the 9 variables, only five variables were found to be statistically significant at the
10% significance level ( shown in bold): PERCHAN, POPDEN, POPELDER, HUDEN,
and PPHH. These variables, therefore, serve as predictors of fatal crashes. Two
statistically significant variables, PERCHAN and HUDEN, are positively associated with
fatal crashes, while the other three variables are negatively related with fatal crashes.
Variable Coefficient Standard Error t- statistics p- value
Constant 2.4299 17.345 0.140 0.889
PERCHAN 0.0082 0.004 2.054 0.040
POPDEN - 0.0004 0.000 - 1.885 0.059
POPELDER - 0.1258 0.041 - 3.033 0.002
POPYOUNG 0.1141 0.202 0.565 0.572
POPMINOR 0.0009 0.014 0.067 0.947
HUDEN 0.0033 0.001 4.782 0.000
PPHH - 2.5289 1.224 - 2.066 0.039
EMPLOY 0.0428 0.174 0.247 0.805
MTT - 0.0258 0.046 - 0.564 0.573
α ( overdispersion parameter) 1.9937 0.513 3.886 0.000
Number of observations
Log- likelihood at zero
Log- likelihood at convergence
87
- 385.4672
- 143.3673
Table 9: Negative Binomial Model Estimation Results of Fatal Crashes with
Complete Set of Predictors
20
Table 10 shows the results of three new models retaining significant predictor variables for
fatal crashes by jurisdiction in Arizona. The table also compares these models to previously
reported and aggregate fatal crash models estimated through other research efforts. It should
be noted that the effort by Van Schalkwyk et al. in 2006 used Traffic Analysis Zones ( TAZ)
as the unit of analysis, and not jurisdiction. With that said, however, the explanatory power
of the Van Schalkwyk model is 75% compared to about 15% for the ‘ best’ model developed
in this effort ( Model 3).
Fatal Crash Models
Existing Models New Models
Variable De Guevara
et al. 2004
Van Schalkwyk
et al. 2006
Model 1 Model 2 Model 3
Constant 0.652 0.017 7.7549 6.49361
POPDEN 0.050782 - 0.0006 - 0.0004
POPMINOR - 5.18194 0.319
INTDEN - 4.81647 - 0.0924
PERCHAN 0.005736 0.004494 0.006366
HUDEN 0.003984 0.002577 0.003154
POPELDER - 0.16036 - 0.13637
PPHH - 2.30763 - 1.96688
PNF_ 0111* 1.762
PNF_ 0512** 1.389
POP00_ 15*** 0.000263
Log-likelihood
- 394.882 N/ A - 149.847 - 145.369 - 143.801
Pseudo R2 N/ A 0.75 0.1147 0.1412 0.1504
* PNF_ 0111 = Proportion ( of total road mileage) of urban and rural interstates in jurisdiction; ** PNF_ 0512 = Proportion of freeways
and expressways in jurisdiction; *** POP00_ 15 = Population aged 0 to 15 years old in jurisdiction.
Table 10: Three New Fatal Crash Models and Comparison to Previously
Estimated Models
This result is partially explained by the fact that variability is lost with increasing levels of
aggregation, and thus the ability to explain variability is also lost. Jurisdictions are cer-tainly
more aggregated than Traffic Analysis Zones. The second important reason is that
the questionnaire administered as part of this research aimed to capture many of the impor-tant
variables that were thought to help explain variation in safety risk across jurisdictions.
Because of the poor overall response rate, and incomplete surveys among those who did
respond, the opportunity to capture additional explanatory variables was missed. As is the
case for most surveys, response rates are directly proportional to the ease of providing the
information, the motivation of the respondent, the frequency of follow- ups, and the ability
for the survey team to assist when possible. Improving response rates for future surveys of
this type would require additional resources to enable these critical elements.
21
Procedure to Apply the Safety Incentive or Safety Target
Forecasting Model
Model 3 shown in Table 10 can be used to predict fatal crashes; however, the precision of
this model is quite low. In other words, for any given set of predictors, there is a large
amount of unexplained variability in the number of fatal crashes occurring within a
jurisdiction. Regardless of the questionable precision of the model, the following
procedure reveals how safety forecasting is performed with this or a similar model.
1. Collect variables needed to run models: All model variables need to be collected for
the jurisdiction being analyzed. The five variables needed to forecast fatal crashes include
POPDEN, PERCHAN, HUDEN, POPELDER, and PPHH ( see Table 1 for a description
and measurement units of these predictor variables).
2. Generate the expected crash counts in a spreadsheet program ( such as Microsoft
Excel) or database management software program ( such as Microsoft Access): The
simple equation derived from the logarithmic negative binomial regression model
estimation results presented in the previous section is used to calculate the expected fatal
crash count ( e. g., pedestrian, total, fatal, etc.) by jurisdiction in the base year and the
incentive year ( e. g., an incentive is given if the jurisdiction meets safety targets in two
years). The model predicts the expected ( mean for all jurisdictions with these predictors)
count of fatal crashes expected per year.
A spreadsheet model can be simply set up in Excel that uses the negative binomial
prediction equation, E( yi)= exp Σβjxij , and the estimated coefficients shown for
Model 3 in Table 10.
Table 11 shows a spreadsheet developed in Microsoft Excel for Model 3 using a
hypothetical jurisdiction in the Base year and after years 1 and 2. Shown in the table are
the values of the predictor variables, reflecting growth and change in the predictor
variables expected during a two year time horizon. For example, the 10- year population
growth rate is expected to increase from 55% to 59% by year 2. Population density is
expected to increase from the base year of 150 to 160 persons per square mile.
Predictor Values
Coefficient Jurisdiction A: Base Jurisdiction A: Year 1 Jurisdiction A: Year 2
constant 6.49361 n/ a n/ a n/ a
POPDEN - 0.0004 150 155 160
POPCHANGE 0.006366 55 57 59
HUDEN 0.003154 150 150 150
POPELDER - 0.13637 10 12 14
PPHH - 1.96688 2 2.05 2.1
Fatal Crash Prediction 7.09 4.95 3.45
Table 11: Example 1: Excel Prediction Spreadsheet for Fatal Crash
Prediction Model
22
In example 1 ( Table 11), the predicted number of fatal crashes is expected to decrease
from 7.09 to 3.45 crashes in year 2. Thus, without any safety investments, fatal crashes in
Jurisdiction A will be reduced by approximately 3.5 fatal crashes. Safety targets for this
jurisdiction should be set appropriately to account for the natural reduction in fatal
crashes.
Example 2, shown in Table 12, shows Jurisdiction B growing rapidly. Its elderly
population is expected to decrease by 2% over the next 2 years, while the 10- year growth
rate is expected to increase by 25%. In the base year 14.46 fatal crashes are expected,
while in year 2, 22.27 fatal crashes are expected. Thus, approximately 7 additional fatal
crashes are expected in Jurisdiction B based on growth trends alone. In this case a safety
target to maintain 14 crashes in year 2 would be extremely aggressive and would require
a significant safety investment.
Predictor Values
Coefficient Jurisdiction B: Base Jurisdiction B: Year 1 Jurisdiction B: Year 2
constant 6.49361 n/ a n/ a n/ a
POPDEN - 0.0004 75 75 75
POPCHANGE 0.006366 55 65 80
HUDEN 0.003154 150 150 150
POPELDER - 0.13637 5 4 3
PPHH - 1.96688 2 2 2
Fatal Crash Prediction 14.46 17.66 22.27
Table 12: Example 2: Excel Prediction Spreadsheet for Fatal Crash
Prediction Model
3. Incorporate modeling results into incentive program: The modeling results in Table
11 predict that fatal crashes will decrease as a result of projected growth in the
jurisdiction and without any safety investments. Thus, safety investments should be
expected to improve safety above and beyond that expected from growth alone and be the
result of effective safety investments. Thus, Jurisdiction A might be expected to show a
reduction in fatal crashes to less than expected, say one or two crashes, while Jurisdiction
B ( Table 12) might be allowed to show an increase of three crashes over the base year.
The structuring of any incentive program, of course, would be devised in the state and
administered by the appropriate agencies and/ or stakeholders.
4. Calibration to Local Conditions: With an improved model ( not one with low
explanatory power), a calibration procedure will be conducted to translate the expected
reduction/ increase in crashes to the observed counts of crashes in a jurisdiction. This
calibration procedure will be developed along with improved models in the future.
23
Conclusions and Recommendations
The data used in this research were obtained from ADOT and the U. S. Census Bureau,
and were compiled for the year 2000. A significant effort was undertaken to collect a host
of additional and important explanatory variables to improve the safety prediction model
( see Appendix A), by mailing a survey to all jurisdiction representatives in Arizona.
Many important exposure- related variables, such as road mileage by functional class,
number and type of schools, number of intersections ( signalized or stop- controlled), and
weather- related variables were sought via the survey and were ultimately unavailable.
This set of additional variables represents important predictors of safety, and fatal crashes
in particular. Unfortunately, the lack of a complete set of predictors undermined the
modeling effort.
The statistical modeling results reflect the exclusion of important variables and will lead
to imprecise predictions of fatal crash frequencies. As shown in Table 10, the ‘ best’ model
in this effort produced a model with an R- Square value of approximately 15% –
suggesting that 15% of the variation in fatal crashes across jurisdictions in Arizona is
explained by the set of predictors in the model. Initial efforts in NCHRP 8- 44 ( by the
same authors of this report) have produced similar models with explanatory power above
75%. These models have included many of the predictors sought in the questionnaire
shown in Appendix A and also shown in Table 13.
While this report provides an analytical procedure for predicting fatal crash frequencies
using a predictive model ( see Table 11 and Table 12), its use is not recommended due to
lack of explanatory power and precision of the model. These model deficiencies lead to
the following problems:
1. The variability across jurisdictions with a similar set of predictor values will be
large. Thus, the predicted fatal crash frequency will represent the mean value of
a highly dispersed distribution of values.
2. Problem 1 above leads to a dilemma of dealing with the dispersion not explained
by the model. A Bayesian correction of sorts, for example, could be used if
known important variables were not missing; however, a Bayesian correction is
problematic in the absence of known important explanatory variables.
3. When an observed fatal crash count in a jurisdiction is not close to the predicted
fatal crash count in the base year a remedy is not known. The difference could be
due to safety deficiencies, due to omitted important predictor variables, or due to
mostly random and unknown effects. The missing important predictor variables
need to be minimized.
4. Problems of omitted variables— well known to the econometrics community—
will bias model predictions ( see Kim et al. 2006a and 2006b and Washington et
al. 2003).
The recommendation is to supplement this report with NCHRP 8- 44- 2 findings when
they become available in April of 2009. The objectives of this NCHRP project— led by
Dr. Simon Washington— are nearly the same as those of this research effort except that
24
the NCHRP project is for a national audience. The objectives of this NCRHP research,
and the similarity to this ADOT project, can be seen at
http:// www. trb. org/ TRBNet/ ProjectDisplay. asp? ProjectID= 919.
It is anticipated that a more complete set of predictors, currently being developed for
NCHRP 8- 44- 2 for Pima and Maricopa counties in Arizona, will yield a more precise and
reliable model for the purpose of devising safety incentives— at least for all jurisdictions
in the MAG and PAG regions. Table 13 shows a sample of some of the predictor
variables that will be available in project 8- 44- 2. Compared to the data available in this
effort, the current effort does not have variables related to weather, to high- risk non-motorized
populations, to speeds and design standards, or to conflicts. Again, the intent
was to capture many of these variables through the questionnaire administered as part of
this project, but poor response rates resulted in a genuine lack of useful data which lead
to the inability to estimate precise forecasting models.
Major Contributing Factor Potential Aggregate ( TAZ level) Variables that may capture
effect of Major Factor ( assumes time scale is year)
Weather Proportion of wet pavement days per year
Proportion of icy pavement days per year
Proportion of snow days per year
Proportion of fog/ reduced visibility days per year
Proportion of sunny days per year
High risk driving populations
Population/ number of licensed drivers
Proportion of population between 16 and 24
Proportion of population over 60
Number of DUI arrests
Employed/ unemployed workers
High risk non motorized
populations
Number of crosswalks
Number of schools ( elementary, middle, high, college)
Percentage/ mileage of sidewalks ( of street mileage)
Percentage/ mileage of bicycle facilities
Speed, design standards of
facilities, and access control
Total street mileage
Proportion of local road mileage
Proportion of collector road mileage
Proportion of arterial road mileage
Proportion of rural highway mileage ( urban/ rural)
Proportion of interstate ( urban and rural)
Conflicts Number/ proportion of signalized intersections
Number/ proportion of stop- controlled intersections
Intersection density
Total area
Table 13: Description of Important Predictor Variables for Safety
Forecasting Model
It is anticipated that NCHRP 8- 44- 2 will produce statistical models with superior pre-dictive
ability and for numerous safety outcomes in addition to fatal crashes. For example,
in addition to fatal crash models, it is anticipated that 8- 44- 2 will produce statistical
models able to forecast total accidents, property damage accidents, incapacitating injury
and fatal crashes, night- time crashes, pedestrian crashes, injury crashes, and bicycle-related
crashes. Thus, an incentive or target program that sets targets across a broad range
of crash outcomes, not just fatal crashes, could be supported with such models.
25
Finally, while the goals and objectives are quite complementary, it is important to note
that the NCHRP 8- 44- 2 effort will not result in the ability to forecast crash outcomes
outside of the MAG and PAG regions. Thus, a safety incentive or target program cannot
be supported statewide, but instead only in these two major regions.
To support a statewide safety incentive or safety target program, the data needed to
estimate these models would need to be made available and/ or collected. Data collection
efforts would be needed in jurisdictions throughout the state including tribes, counties,
and townships.
26
27
Appendix A: Questionnaire Sent to Jurisdictions
Thank you for taking the time to complete the following survey. The information you provide will be used to
help us develop fatality crash models to predict a fair and reasonable fatality rate for each jurisdiction. Please
note that the information you provide should be based on the year of 2000.
1. Your city or town name:
2. Road mileage information by road functional classification:
􀁹 Total mileage of all functional classes of roads:
􀁹 Total mileage of principal arterial interstate:
􀁹 Total mileage of principal arterial expressway:
􀁹 Total mileage of principal arterial:
􀁹 Total mileage of minor arterial:
􀁹 Total mileage of major collector rural:
􀁹 Total mileage of minor collector rural:
􀁹 Total mileage of urban collector:
􀁹 Total mileage of local streets:
3. School information
􀁹 Number of elementary schools:
􀁹 Number of middle schools:
􀁹 Number of high schools:
4. How many intersections and bus stops were there within your city ( or town) in 2000?
􀁹 Intersections: 􀁹 Bus stops:
5. How many people had driver licenses in 2000?
6. How many tickets were issued in 2000?
7. How many tickets related to speeding were issued in 2000?
8. How many DUI related accidents occurred in 2000?
9. Weather information:
􀁹 What is the annual average precipitation in 2000? inches
􀁹 What is the annual average snowfall in 2000? inches
Please return this survey by November 10th by fax on 480- 965- 0557 ( Do- Gyeong Kim) or via email at
dokkang@ u. arizona. edu.
28
Appendix B: Arizona Population and Population Change
Statistics by Jurisdiction ( 2000)
Jurisdictions Population in
1990
Population in
2000 Change (%)
Bullhead City 21,951 33,769 53.8
Colorado City 2,426 3,334 37.4
Kingman 12,722 20,069 57.8
Mohave County
Lake Havasu City 24,363 41,938 72.1
La Paz County Parker 2,897 3,140 8.4
Quartzsite 1,876 3,354 78.8
San Luis 4,212 15,322 263.8
Somerton 5,282 7,266 37.6
Wellton 1,066 1,829 71.6
Yuma County
Yuma 56,966 77,515 36.1
Marana 2,187 13,556 519.8
Oro Valley 6,670 29,700 345.3
Sahuarita 1,629 3,242 99.0
South Tucson 5,171 5,490 6.2
Pima County
Tucson 405,371 486,699 20.1
Eagar 4,025 4,033 0.2
Saint Johns 3,294 3,269 - 0.8
Apache County
Springerville 1,802 1,972 9.4
Flagstaff 45,857 52,894 15.3
Fredonia 1,207 1,036 - 14.2
Page 6,598 6,809 3.2
Coconino County
Williams 2,532 2,842 12.2
Holbrook 4,686 4,917 4.9
Pinetop- Lakeside 2,422 3,582 47.9
Show Low 5,020 7,695 53.3
Snowflake 3,679 4,460 21.2
Taylor 2,418 3,176 31.3
Navajo County
Winslow 9,279 9,520 2.6
Camp Verde 6,243 9,451 51.4
Chino Valley 4,837 7,835 62.0
Clarkdale 2,144 3,422 59.6
Cottonwood 5,918 9,179 55.1
Jerome 403 329 - 18.4
Prescott 26,592 33,938 27.6
Prescott Valley 8,904 23,535 164.3
Yavapai County
Sedona 7,720 10,192 32.0
29
Jurisdictions Population in
1990
Population in
2000 Change (%)
Maricopa County Avondale 16,169 35,883 121.9
Buckeye 4,436 6,537 47.4
Carefree 1,657 2,927 76.6
Cave Creek 2,925 3,728 27.5
Chandler 89,862 176,581 96.5
El Mirage 5,001 7,609 52.1
Fountain Hills 10,030 20,235 101.7
Gila Bend 1,747 1,980 13.3
Gilbert 29,122 109,697 276.7
Glendale 147,864 218,812 48.0
Goodyear 6,258 18,911 202.2
Guadalupe 5,458 5,228 - 4.2
Litchfield Park 3,303 3,810 15.3
Mesa 288,104 396,375 37.6
Paradise Valley 11,773 13,664 16.1
Peoria 50,675 108,364 113.8
Phoenix 983,392 1,321,045 34.3
Queen Creek 2,667 4,316 61.8
Scottsdale 130,075 202,705 55.8
Surprise 7,122 30,848 333.1
Tempe 141,993 158,625 11.7
Tolleson 4,434 4,974 12.2
Wickenburg 4,515 5,082 12.6
Youngtown 2,542 3,010 18.4
Gila County Globe 6,062 7,486 23.5
Hayden 909 892 - 1.9
Miami 2,018 1,936 - 4.1
Payson 8,377 13,620 62.6
Winkelman 676 443 - 34.5
Pinal County Apache Junction 18,092 31,814 75.8
Casa Grande 19,076 25,224 32.2
Coolidge 6,934 7,786 12.3
Eloy 7,211 10,375 43.9
Florence 7,321 17,054 132.9
Kearny 2,262 2,249 - 0.6
Mammoth 1,845 1,762 - 4.5
Superior 3,468 3,254 - 6.2
30
Jurisdictions Population in
1990
Population in
2000 Change (%)
Cochise County Benson 3,824 4,711 23.2
Bisbee 6,288 6,090 - 3.1
Douglas 13,137 14,312 8.9
Huachuca City 1,782 1,751 - 1.7
Sierra Vista 32,983 37,775 14.5
Tombstone 1,220 1,504 23.3
Willcox 3,122 3,733 19.6
Graham County Pima 1,725 1,989 15.3
Safford 7,359 9,232 25.5
Thatcher 3,763 4,022 6.9
Greenlee County Clifton 2,840 2,596 - 8.6
Duncan 662 812 22.7
Santa Cruz County Nogales 19,489 20,878 7.1
Patagonia 888 881 - 0.8
31
Appendix C: Arizona Population Density by Jurisdiction ( 2000)
Jurisdiction Land Area Population Population
Density
Bullhead City 45.2 33,769 746.6
Colorado City 10.5 3,334 317.3
Kingman 30.0 20,069 669.7
Mohave County
Lake Havasu City 43.0 41,938 974.4
La Paz County Parker 22.0 3,140 142.8
Quartzsite 36.3 3,354 92.4
San Luis 26.4 15,322 579.5
Somerton 1.3 7,266 5,483.2
Wellton 2.5 1,829 727.3
Yuma County
Yuma 106.7 77,515 726.8
Marana 72.7 13,556 186.6
Oro Valley 31.8 29,700 933.1
Sahuarita 15.2 3,242 213.2
South Tucson 1.0 5,490 5,446.6
Pima County
Tucson 194.7 486,699 2,500.1
Eagar 11.3 4,033 355.6
Saint Johns 6.6 3,269 494.8
Apache County
Springerville 11.5 1,972 170.8
Flagstaff 63.6 52,894 831.9
Fredonia 7.4 1,036 139.7
Page 16.6 6,809 410.5
Coconino County
Williams 43.5 2,842 65.3
Holbrook 15.4 4,917 318.4
Pinetop- Lakeside 11.3 3,582 318.1
Show Low 27.9 7,695 276.2
Snowflake 30.8 4,460 144.8
Taylor 24.6 3,176 129.1
Navajo County
Winslow 12.3 9,520 773.1
Camp Verde 42.6 9,451 222.0
Chino Valley 18.6 7,835 421.6
Clarkdale 7.3 3,422 466.9
Cottonwood 10.7 9,179 860.3
Jerome 0.7 329 462.1
Prescott 37.1 33,938 915.6
Prescott Valley 31.7 23,535 742.0
Yavapai County
Sedona 18.6 10,192 548.0
32
Jurisdiction Land Area Population Population
Density
Maricopa County Avondale 41.3 35,883 869.7
Buckeye 145.8 6,537 44.8
Carefree 8.8 2,927 330.8
Cave Creek 28.2 3,728 132.0
Chandler 57.9 176,581 3,050.5
El Mirage 9.7 7,609 786.8
Fountain Hills 18.2 20,235 1,113.8
Gila Bend 22.8 1,980 86.7
Gilbert 43.0 109,697 2,553.7
Glendale 55.7 218,812 3,929.5
Goodyear 116.5 18,911 162.4
Guadalupe 0.8 5,228 6,813.9
Litchfield Park 3.1 3,810 1,216.6
Mesa 125.0 396,375 3,171.3
Paradise Valley 15.5 13,664 881.7
Peoria 138.0 108,364 2,781.9
Phoenix 474.9 1,321,045 167.3
Queen Creek 25.8 4,316 1,100.4
Scottsdale 184.2 202,705 443.9
Surprise 69.5 30,848 3,959.4
Tempe 40.1 158,625 894.1
Tolleson 5.6 4,974 441.7
Wickenburg 11.5 5,082 2,296.1
Youngtown 1.3 3,010 726.8
Gila County Globe 18.0 7,486 415.5
Hayden 1.3 892 707.1
Miami 1.0 1,936 2,008.0
Payson 19.5 13,620 699.6
Winkelman 0.7 443 612.3
Pinal County Apache Junction 34.2 31,814 929.3
Casa Grande 48.2 25,224 523.7
Coolidge 5.0 7,786 1,549.1
Eloy 71.7 10,375 144.8
Florence 8.3 17,054 2,056.2
Kearny 2.8 2,249 805.4
Mammoth 1.1 1,762 1,626.5
Superior 1.9 3,254 1,684.6
33
Jurisdiction Land Area Population Population
Density
Cochise County Benson 35.7 4,711 131.9
Bisbee 4.8 6,090 1,266.3
Douglas 7.7 14,312 1,852.7
Huachuca City 2.8 1,751 626.5
Sierra Vista 153.5 37,775 246.1
Tombstone 5.6 1,504 894.1
Willcox 6.0 3,733 622.3
Graham County Pima 2.5 1,989 787.0
Safford 7.9 9,232 1,166.1
Thatcher 4.4 4,022 919.4
Greenlee County Clifton 14.9 2,596 174.8
Duncan 2.6 812 317.6
Santa Cruz County Nogales 20.8 20,878 1,002.1
Patagonia 1.2 881 738.7
34
35
References
Abdel- Aty, M. A. and A. E. Radwan. 2000. Modeling traffic accident occurrence and
involvement. Accident Analysis and Prevention 32: 633 – 642.
Arizona Department of Transportation. Arizona Motor Vehicle Crash Facts 2000.
Prepared by the Motor Vehicle Division in cooperation with the Traffic Records Section.
Phoenix, 2001.
Chin, H. C. and M. A. Quddus. 2003. Applying the random effect negative binomial
model to examine traffic accident occurrence at signalized intersections. Accident
Analysis and Prevention 35: 253– 259.
Greene, W. 2000. Econometric Analysis. Upper Saddle River, NJ: Prentice Hall.
Harwood, D. W., F. M. Council, E. Hauer, W. E. Hughes, and A. Vogt. 2000. Prediction of
the Expected Safety Performance of Rural Two- Lane Highways. FHWA- RD- 99- 207.
Washington D. C.: Federal Highway Administration.
Hauer, E., J. C. N. Ng, and J. Lovell. 1988. Estimation of safety at signalized
intersections ( with discussions and closure). Transportation Research Record 1185: 48- 61.
Joshua, S. and N. Garber. 1990. Estimating truck accident rate and involvement using
linear and Poisson regression models. Transportation Planning and Technology 15: 41- 58.
Jovanis, P. and H. Chang. 1986. Modeling the relationship of accidents to miles traveled.
Transportation Research Record 1068: 42- 51.
Kim, D.- G., J. Oh, and S. Washington. 2006a. Modeling crash types: new insights into the
effects of covariates on crashes at rural intersections. ASCE Journal of Transportation
Engineering 132 ( 4): 282- 292.
Kim, D.- G., Y. Lee, S. Washington, and K. Choi. 2006b. Modeling crash outcome
probabilities at rural intersections: application of hierarchical binomial logistic models.
Analysis and Prevention 39 ( 1): 125- 134.
Ladron de Guevara, F. and S. Washington. 2004. Forecasting crashes at the planning
level: a simultaneous negative binomial crash model applied in Tucson, Arizona.
Transportation Research Record 1897: 191- 199.
Lord, D., S. Washington, and J. Ivan. 2004. Poisson, Poisson- Gamma, and zero- inflated
regression models of motor vehicle crashes: balancing statistical fit and theory. Accident
Analysis and Prevention 37 ( 1): 35- 46.
36
Lyon, C., J. Oh, B. Persaud, S. Washington, and J. Bared. 2003. Empirical investigation
of interactive highway safety design model accident prediction algorithm: rural
intersections. Transportation Research Record 1840: 78– 86.
Miaou, S., P. Hu, T. Wright, A. Rathi, and S. Davis. 1992. Relationship between truck
accidents and highway geometric design: a Poisson regression approach. Transportation
Research Record 1376: 10– 18.
Mitra, S., H. C. Chin, and M. A. Quddus. 2002. Study of intersection accidents by
maneuver type. Transportation Research Record 1784: 43– 50.
Oh, J., C. Lyon, S. Washington, B. Persaud, and J. Bared. 2003. Validation of the FHWA
crash models for rural intersections: lessons learned. Transportation Research Record
1840: 41– 49.
Oh, J., S. Washington, and K. Choi. 2004. Development of accident prediction models for
rural highway intersections. Transportation Research Record 1897: 18- 27.
Persaud, B. and T. Nguyen. 1998. Disaggregate safety performance models for signalized
intersection on Ontario Provincial roads. Transportation Research Record 1635: 113– 120.
Shankar, V., F. Mannering, and W. Barfield. 1995. Effect of roadway geometric and
environmental factors on rural freeway accident frequencies. Accident Analysis and
Prevention 27 ( 3): 371– 389.
Stutts, J., W. Hunter, and W. Pein. 1996. Pedestrian- vehicle crash types: an update.
Transportation Research Record 1538: 68– 74.
U. S. Bureau of the Census. Census Data for State of Arizona, 2000. Washington D. C.,
2003.
Van Schalkwyk, I., M. Sudeshna, and S. Washington. 2006. Incorporating weather into
region- wide safety planning prediction models. Proceedings of the 85th Transportation
Research Board Annual Meeting.
Vogt, A. and J. Bared. 1998. Accident Prediction Models for Two- Lane Rural Roads:
Segments and Intersections. FHWA- RD- 98- 133. Washington D. C.: Federal Highway
Administration.
Vogt, A. 1999. Crash Models for Rural Intersections: Four- Lane by Two- Lane Stop-
Controlled and Two- Lane by Two- Lane Signalized. FHWA- RD- 99- 128. Washington D. C.:
Federal Highway Administration.
Washington, S., J. Metarko, I. Fomunung, R. Ross, F. Julian, and E. Moran. 1999. An
inter- regional comparison: fatal crashes in the southeastern and non- southeastern United
States: preliminary findings. Accident Analysis & Prevention 31 ( 102): 135- 146.
37
Washington, S., M. Karlaftis, and F. Mannering. 2003. Statistical and Econometric
Methods for Transportation Data Analysis. Boca Raton, FL: Chapman and Hall.
Washington, S., M. Meyer, I. van Schalkwyk, E. Dunbaugh, S. Mitra, and M. Zoll. 2006.
Incorporating Safety into Long Range Transportation Planning. NCHRP 8- 44.
Washington D. C.: Transportation Research Board.
White, D. and S. Washington. 2001. Safety restraint use rate as a function of law
enforcement and other factors: preliminary analysis. Transportation Research Record
1779: 109- 115.
Zellner, A. 1962. An efficient method of estimating seemingly unrelated regressions and
tests for aggregation bias. Journal of the American Statistical Association 57 ( 298): 348–
368.